Two healing-factor immortals — Wolverine's adamantium and superior combat skill give him the narrow edge.
The ultimate 'what happens when two unkillable fighters try to kill each other?' Neither can permanently die, both regenerate from virtually any wound, and both are elite combatants with centuries of experience.
Wolverine's edge comes from adamantium. His claws and skeleton are indestructible, while Deadpool's weapons (katanas, guns) are conventional and can be broken. In close combat, Wolverine's claws deal more permanent structural damage than Deadpool's healing factor can easily repair — adamantium cuts stay open longer because the body can't push the unbreakable metal out.
Deadpool is arguably the more creative fighter — his fourth-wall awareness and chaotic combat style make him unpredictable. But Wolverine's raw combat instinct, honed over centuries, and his adamantium-reinforced skeleton give him the physical advantage in every exchange.
Deadpool's healing factor is arguably stronger than Wolverine's, he has more weapon variety, and his unpredictable fighting style makes him difficult to counter. Wade has also shown awareness of narrative conventions that gives him meta-tactical advantages.
Adamantium claws cut deeper and heal slower than Deadpool's conventional weapons. Wolverine's combat instinct is more refined. His indestructible skeleton means he can take hits that would incapacitate Deadpool (spine breaks, skull fractures). Logan's berserker rage gives him intensity that even Wade's chaos can't match.
Wolverine wins the majority through adamantium superiority and more refined combat skill. But neither can permanently finish the other, making this an endless cycle of violence, regeneration, and increasingly inappropriate banter.
Deadpool also fights
Wolverine also fights