this is a good match. Both sides are pretty much evenly matched. I think though Wolverine takes the victory in this case. Batman is the greatest hero when it comes to overcomming great odds. He has always been superb at figuring out a way to bring overwhelming foes to his level. Woleverine fights on batman's level. He relies soley on physical attributes, and reaction time. Batman has the forsight, and intelligence. However this would be a battle that would be settled through fighting abilities, and physical capabilities. Batmans intelligence may be an advantage in some way, but wolverine has the upper hand on fighting tactics. Batman has his gadgets, wolverine has his indestructible claws, healing factor, and adamantium plated skeleton.
Batman wouldnt be able to endure punching steel for very long,and he wouldnt be able to risk getting to close to wolvies claws for to long he would have to resort to other means of fighting. This is where his intelligence comes to play, however wolverine may not be the brightest bulb on the tree, but he has fought some of the most brilliant villians around, so he would be able to deduce,and fight through what batman could throw at him for a little while. Pretty much everything that batman can do, he couldnt do when fighting wolverine. It would turn out to be a bar knuckled braw. It batman could incoorperate his martial arts training, and stay clear minded he may be able to pull it off, but what gives wolverine the victory hands down is two words (BESERKER BARAGE ) when wolverine goes beserker NO ONE is safe.