Deadpool would win in the end, because he doesn't just regenerate - he can't die. His existence in the Marvel universe has been written into it's reality and even if utterly destroyed, he HAS to be recreated. His insanity is based on the numerous head wounds and his merging with other people, but also because essentially he is a universal constant. .
Doesn't make much sense but I will take your word for it. Minus the alter reality thing I believe Wolverine would still win in a battle. I don't know how long it takes Deadpool to regenerate but it will give Wolverine plenty time to 'escape'.
Wolverine, except for when he was getting poisoned by the adamantine, heals extremely fast. It doesn't seem to matter where the energy to heal comes from, or how badly injured he is - he just heals. Deadpool's healing varies depending on if he's happy or angry. If he is feeling a negative emotion he heals slower. This is from the comics, so subject to writer's whim in some episodes. With that in mind, and forgetting about the more fantastical Deadpool stories, Wolverine would win.
They each can heal from everything in the other's arsenal, so its a wash if you just stick them in an arena.
Outside of the arena, I expect Wolverine to hold the upper hand thanks to a faster healing factor, and the fact he can call on people liable to know how to end deadpool's regeneration.