if they were locked in a cage, or up close space, no holds barred to the death fight Wolverine would take it. Wolverine is a samurai, a spy, a cowboy, a soldier, a brawler, a ninja, and lived a long time as an animal in the wild. on top of that Batman aint gonna box a dude with a metal skeleton who take an insane amount of pain all the times and win. Wolverine is on kill most of the time and has more bodies than the there are people in Rhode Island. he would take this no question.
The only hope Batman has, is if he actually went for the kill, and used his ninja/martial arts training and went for the throat, used the shuriken to blind dude, the fins on his forearms throw him around and choke him into unconsciousness. Logan can get sloppy due to his healing factor and gets throw around a lot. Also, Wolverine can drown, so it goes without saying you can probably choke him out and then finish him, like pull out his guts, his heart, brain etc. Batman would need to go into killer mode, and he dont do that. so that would be it.