Let’s compare both the opponents to see how they match up
First, the physical aspect
Batman (Bruce Wayne) -
Stats:
Gender Male
Height 6' 2"
with armour 6' 5"
Weight 210 lbs (95 kg)
Eyes Blue
Hair Black
Universe New Earth
Place of Birth Gotham City
Deadpool (Wade Wilson) -
Stats:
Gender Male
Height 6' 2"
Weight 210 lbs (95 kg)
Eyes Brown
Hair Bald (formerly brown or sometimes shown to have been blond)
Universe Earth-616
Place of Birth Canada
In terms of physical stats they are equals.
Now, let’s compare their powers and abilities.
BATMAN:
Powers and Abilities
Abilities
Indomitable Will: Although he has no superhuman powers, Batman's unstoppable determination and strength of will make him an extremely formidable opponent. This makes him able to function while tolerating massive amounts of physical pain, and also allows him to resist telepathy or mind control. His willpower is strong enough to operate a Green Lantern Ring when necessary.
Intimidation: It is widely known that Batman has the ability to instill fear in others, to the extent that even the people that know him best are intimidated by him, Batman regularly forcing common criminals to flee in terror despite there being no evidence that he would actually kill anyone. Even those who aren't afraid of the likes of Superman fear Batman. His ability to inspire great fear made him eligible for induction into the Sinestro Corps, although he was able to fight off the power ring's control.
Interrogation: Batman is adept in interrogation techniques, often using law enforcement methods as well as torture. Several methods seen include hanging a person over the edge of a building by one leg or chaining a person upside down and beating them. He usually just plain uses his frightening appearance to get answers. "Fear is an excellent motivator" he once said.
Peak Human Condition: Through intense training, specialized diet, and biofeedback treatments, Batman represents the pinnacle of human physical prowess. His physical attributes exceeded that of any Olympic level athlete that has ever completed. Strength, speed, stamina, agility, reflexes and coordination are at peak human perfection. Batman began his physical and mental conditioning when he was 11 and then intense physical training and weight lifting at age 12. He has mastered full body control by the time he was 18. Bruce Wayne, since the age of 15, has created a strict diet to enable his body to develop and operate at its most proficient, along with biofeedback treatments (using portable/non portable machines to stimulate muscles to contraction). Batman has performed amazing physical feats due to his superior physique. He engaged in an intensive regular regimen of rigorous exercise (including aerobics, weight lifting, gymnastics, and simulated combat) to keep himself in peak condition, and has often defeated opponents whose size, strength, or other powers greatly exceeded his own. He has spent his entire life in pursuit of physical perfection and has attained it through constant intensive training and determination.
Peak Human Strength: Batman regularly bench-presses at least 1000 lbs. during his exercise routine. This means he's capable of amazing feats such as punching a SWAT officer through a brick wall.
Peak Human Reflexes: Bruce's reflexes were honed to such a degree that he has caught one of Green Arrow's arrows in mid flight when he tried to shoot him. He has also been able to dodge point blank gunfire.
Peak Human Speed: He could run at speeds comparable to the finest competing athletes.
Peak Human Endurance: His endurance was comparable to that of the finest Olympic Decathlon participant. His lung capacity was so great that he could hold his breath underwater for 3 minutes and 15 seconds. He can survive in the airless vacuum of space for exactly 27 seconds.
Peak Human Agility: His agility was greater than that of a Chinese acrobat and an Olympic gold medalist gymnast. His main phase of movement was Parkour which he learned in France and used that to scale the cities rooftops in an acrobatic manner.
Acrobatics: He is proficient in gymnastics and acrobatics.
Martial Arts: Bruce is well trained in multiple martial arts, he is known as the man who has mastered 127 forms of martial arts. His primary form of combat is an idiosyncratic admixture of Tae Kwon Do, Judo, Muay Thai, Dragon Style Kung Fu, Boxing, Jujitsu, Ninjitsu and Capoeira.
Weaponry: Through his martial arts training, he has become an expert on all melee weapons. Wayne has displayed exceptional sword fighting capability and proficiency with knives, sticks and various other weapons. He practices during his combat sessions to keep his skills intact, but he prefers unarmed combat.
Stealth: His Ninjutsu training has made him a master at stealth and capable of breaching high security facilities without being detected. He is also been able to fool Superman’s super senses.
Marksmanship: Wayne is an expert marksman. He is skilled with throwing projectile weapons, archery and firearms. He has been practicing such skills since the early days of his training and is almost on par with the Green Arrow in terms of accuracy.
Genius Level Intellect: Batman is a brilliant, virtually peerless, detective, strategist, scientist, tactician, and commander; he is widely regarded as one of the keenest analytical minds on the planet. Given his lack of superpowers, he often uses cunning and planning to outwit his foes, rather than simply "out-fighting" them.
Polymath: He has studied Biology, Technology, Mathematics, Physics, Mythology, Geography and History. Gained degrees in Criminal Science, Forensic Sciences, Computer Sciences, Chemistry and Engineering by the time he was 21. He has mastered Diverse Environmental Training, Security Systems, and illusion/sleight of hand by the time he was 23. He gained even more degrees in Biology, Physics, Advanced Chemistry, and Technology by the time he was 25. He had learned Forensic Sciences, Medical Sciences, Expanded Computer and Engineering Sciences, and Expanded Device Pool use of personal powered armor and system, database creation on underworld crime bosses, rogue's gallery foes and other supervillains; improved material sciences for body armor and micro-machinery by the time he was 26. Has also learned Advanced New Development in Forensic and Medical Sciences.
Eidetic Memory: Batman has total recall and can remember anything in great detail.
Investigation: He is widely considered as the World's Greatest Detective, capable of observation, forensic investigation, and inductive and deductive reasoning of the highest caliber. Human intuition is an unlearnable trait and one of Batman's most effective tools. Given any mystery, he can arrive at the correct conclusions with a fraction of the data.
Tactical Analysis: He commonly utilizes cunning tactics to outwit his foes, relying on his plans and experience to outmanoeuvre many of his superhuman friends and adversaries. He is an excellent leader and at times commands the Justice League and the Outsiders, Batman is known as one of the greatest strategists and tacticians in the DC universe, and once even Aquaman stated the same.
Escapology: He has been described as second only to Mister Miracle as an escape artist. He has been seen escaping from a Posey straitjacket in less than 52 seconds, and remarked afterwards that the time was way too slow for him.
Tracking: Trained in hunting techniques by African Bushmen (the Ghost Tribes of the Ten-eyed Brotherhood, among others).
Disguise: Has mastered the art of disguise by the time he was 23. Has further learned expanded disguise techniques by the time he was 26, through various instructions from Alfred. Batman has many aliases he uses to infiltrate the underworld or just to go undercover in public situations. His current aliases are: Matches Malone, Thomas Quigley, Ragman, Detective Hawke, Sir Hemingford Grey, Frank Dixon, Gordon Selkirk, and Mr. Fledermaus.
DEADPOOL:
Powers and Abilities
Powers
Genetically Enhanced Physiology: Deadpool's powers come from the experimentation he was submitted to by the Weapon X program.
Regenerative Healing Factor: Deadpool possesses a superhuman healing factor derived from that of Wolverine that allows him to regenerate damaged or destroyed bodily tissue with far greater speed and efficiency than an ordinary human. Deadpool is able to heal from injuries such as slashes, puncture wounds, bullet wounds, beheading, and severe burns within moments. His healing factor is significantly more powerful than Wolverine's as he can regrow missing limbs and organs and was able to recover after the Hulk liquidated everything from his waist up. His head or any other limb can be reattached using this ability. Even though being beheaded, Deadpool can still move his body normally. Unlike Wolverine's natural healing factor, Deadpool's is mentally driven to a partial extent.
Foreign Chemical Resistance: Deadpool's body is highly resistant to most drugs and toxins. For example, it is extremely difficult, though not impossible, for him to become intoxicated (Blind Al made several references to Deadpool being hung-over since he once drunkenly spoke to the Teletubbies on the TV he was watching). He can, momentarily, be affected by certain drugs (tranquilizers) if exposed to a large enough dosage.
Disease Immunity: The unique regenerative qualities of Deadpool's healing factor also extend to his immune system; he is immune to all diseases, infections, disorders, imperfection, and resistant to elemental extremes.
Immortality: Deadpool's healing factor provides him with an endless lifespan by halting the aging process. His life span is extended to such a degree that an alternate reality version of him was alive and still in business as Deadpool 800 years in the future.
Telepathic Immunity: The healing factor causes his brain to be in a constant state of flux and regeneration, rendering him immune to psychics such as Cable, Emma Frost, and the Red Onslaught.
Possession Resistance: Similar to the telepathic immunity, Deadpool is able to remain in control of himself while supernatural beings are trying to take control of him. During Xaphan's attempt to take control of him, Wade was able to fight for control of his body. No one can touch his soul.
Enhanced Strength: Deadpool is rated as having a superhuman level of strength, capable of lifting 2 tons.
Enhanced Speed: Deadpool can easily reach speeds of 80 mph, and attack faster than the eye can follow.
Superhuman Stamina: Deadpool's musculature generates considerably less fatigue toxins than the muscles of an ordinary human being, granting him superhuman levels of stamina in all physical activities. He can physically exert himself at peak capacity for several days before fatigue takes over.
Superhuman Agility: Deadpool's agility, flexibility, dexterity, balance, and bodily coordination are enhanced to levels that are beyond the natural physical limits of even the finest human athlete.
Superhuman Reflexes: His reflexes are far superior to those of even the finest human athlete. His auto-reflexes allow him to easily dodge gunfire and attacks even when not consciously aware of them.
Superhuman Durability: Deadpool's bone and muscle tissues are augmented to levels that are considerably stronger and harder than human and the tissues are impervious to injury to an extraordinary extent. He possesses golden-proportioned body, and even without training his muscles are brawny and his body shape doesn't change no matter how many calories he intakes.
Abilities
Master Martial Artist: Deadpool is an extraordinary hand-to-hand combatant and is a master in multiple unarmed combat techniques. He has been shown fighting such amazingly skilled fighters as Wolverine and Taskmaster and even defeating them in hand to hand combat. This shows that Deadpool himself is among the most skilled fighters in the Marvel universe, although in some fights it has been attributed to him being unpredictable.
Master Assassin: He is a master of assassination techniques, espionage methods, covert operations, infiltration methods, escape artistry, marksmanship, and is highly skilled with many bladed weapons (frequently carrying two swords strapped to his back) and a number of other weapons including firearms.
Medium Awareness: Possibly as a result of his mental state, he is aware that he is a fictional comic book character, allowing him to break the fourth wall.
Unpredictability: It is difficult for anyone to know what Deadpool will do at any given moment, given that he himself barely knows what he'll do at any given moment. This makes it difficult for most opponents to predict what he will do.
Now, let’s move on to weapons and gadgets/equipments:
BATMAN:
Batman has a ton of weapons and gadgets. I am posting those that are frequently used but not limited to:
Equipment
Batsuit: The costume Batman wears is composed of reinforced Kevlar and a small percentage of titanium; it's bullet-proof and resistant to various types of attack (explosions, impacts, falls, etc...). It's also flame-retarding and insulating. The gloves and the boots are reinforced to rebound the impact of punches and kicks. The gloves have also some metallic blades on their sides. The cape is designed to provide the wearer with controlled gliding functionality with the ability to change directions and heights while in mid-air. The mask has a little percentage of lead, which shields the face of Batman from x-ray powers or x-ray technology, and incorporates an infrared and night visor, auditory sensors and a sonar. The mask is accessorized with some security systems (aggravating gas, electric blasts, etc.), like the utility belt, and integrates a transmitter receiver device de voice and video.
For more info on it you can refer to my answer
Brenden Louis' answer to What are all the batsuits worn by batman in the comics?
Utility Belt: Batman keeps most of his personal field equipment in a signature piece of apparel, a yellow utility belt.The utility belt has a button to call the car in a few appearances on Justice League, and a command for teleportation. Over the years it has contained items such as plastic explosives, nerve toxins, batarangs, smoke bombs, a fingerprint kit, a cutting tool, a grappling hook gun, torches, a "re-breather" breathing device, and lockpicks. Superman had entrusted Batman with a ring made of kryptonite, to be used should the Man of Steel ever need to be reined in (due to being mind-controlled by a villain, etc.). The Kryptonite Ring is contained in a lead pocket, in order to shield Batman from its radiations. The belt has also its own automatic security systems.
Transportation
Batboat
Batcycle
Batmobile
Batplane
Weapons
Batman has access to numerous lethal and non-lethal weapons alongside other devices like Mother Box and Power Ring. I cannot list them all as it would make the answer unnecessarily long. Please refer to:
Brenden Louis' answer to How many weapons does Batman have? List them please.
DEADPOOL:
Equipment
Deadpool's Suit: Deadpool wears a full body tactical suit.
Image Inducer: Deadpool had access to an holographic image inducer that he can use to disguise his true appearance as necessary.
Transportation
Teleportation Device: Deadpool has utilized different teleportation devices to whisk him out of (and occasionally into) danger. Deadpool was able to 'bodyslide' to wherever Cable is present, through Providence. At different periods Deadpool has possessed different teleportation technologies which he sometimes uses for combat.
Weapons
Deadpool's Katanas: Wilson wields a pair of steel katanas. He is able to charge his katanas with an energy field through his suit, increasing the durability of his swords and increasing their cutting power to the point that they can easily cut through objects as hard as diamond.
Other Weapons: Deadpool employs any number of weapons depending on his current assignments. Most often, Deadpool uses multiple types of guns, grenades, swords, sai, and knives. Wade can use any weapon known to man and can learn how to use any weapon in less than five minutes. Wade is mainly seen using a gun or edged weapon, including hammers and axes, though he mostly uses multiple types of swords and knives.
Now, let’s see their weaknesses.
BATMAN:
Weaknesses
Single-Mindedness: Batman's drive to protect Gotham has been used against him on several occasions, most notably when Bane decided to confront Batman only after wearing him down by destroying Arkham Asylum, knowing that his foe would try and capture all the escaped inmates himself and thus push himself to the brink of exhaustion.
Human limitations: Though at peak physical condition, Bruce is still a human and has human limitations.
DEADPOOL:
Weaknesses
Mental state: His healing abilities render his brain unreadable to telepaths, but its constant healing also makes him highly unstable and prone to violent outbursts without the slightest provocation, at least against those he knows could handle. Even with his healing factor, Deadpool can still feel pain from damage taken, although he has a notably high pain tolerance. While it has been shown that Deadpool's condition may not be the source of his instability, it only makes it worse. In several flashbacks to his childhood, he was still shown to be unhinged, and curing his condition did not make him any saner.
Cure for Cancer: Wade's healing factor was specifically designed to replace his bodies cells as fast as they were being destroyed by his illness. Until recently when both his healing factor and illness were removed, should his cancer be cured then his healing factor would be rapidly producing redundant new cells, which, if left unchecked, would cause horrible growths over the body and would eventually explode, as demonstrated on the Super Skrulls with Deadpool's powers.
Phobias: Deadpool has bovinophobia, which is the fear of cows. According to him, cows "scare the *#$% outta me", as he believes their stare to be chilling, like they're "waiting". He may also be scared of chickens, like Domino. During Deadpool's adventure to save the multiverse from the Awareness, it was revealed that his worst fear is to be truly and utterly alone.
VERDICT
The obvious winner of this battle is Batman. There is a reason why Supes calls him the most dangerous man on earth.
