Let's look at this logically, I know hard to do for two fictional characters, but let's try. I love both characters so I don't think character bias is an issue, even though I've been waiting 25 years for a DC/Marvel crossover of these two characters.
powers:
-Batman - none save ninjitsu training (ability to seemingly disappear into the shadows)
-Wolverine - mutant healing factor, admantium claws and coated bones, hightened animal senses (smell especially)
physical agility:
-Batman - above olympic level athlete, worlds most accomplished martial artist trained in most all fighting styles known to man, keen reflexes and dead aim (throwing batarangs and batropes while falling through the air)
-Wolverine - enhanced strength, accomplished martial artist, military training
intelligence:
- Batman - no nonsense natural leader, world most brilliant detective, expert chemist, insight into psychology and criminal justice, brilliant inventor
-Wolverine - good stratigist, tracker and assasin skills, natural but sometimes unwilling leader
gadgetry:
-Batman - Batman has his various arsenal of gadgets from the famed batmobile to the items carried in his utility belt. His natural ability to invent items ensures that if he doesn't have the item he needs to tackle an opponent, he has the means to escape. This is a stratigic plan to ensure the next time he faces the foe he will be prepaired.
-Wolverine - none so much relying mainly on his powers and fighting ability, occasionally using a weapon such as a sword
transportation:
-Batman - Batmobile, Batboat, Batplane, Batjet, Batcopter, Bat toilet seat, you name it this billionaire has it in a bat form
-Wolverine - Motorcycle, jeep, X-Jet
Mentality:
they're both crazy
-Batman - unstoppable fighter, won't give up unless unconsious and will sacrifice himself inorder to entice the opponent to thinking the fight is won
-Wolverine - pretty much the same
summary: Wolverine while having somewhat superior strength and being almost unstoppable due to his quick healing factor would edge out Batman in a strickly hand to hand combat situation, not because of skill but because of his healing ability. Every wound Batman would make would quickly heal, so he would eventually tire out. Alas Batman's superior intellegence would hint to this fact after seeing the first wound heal, and the tools of his trade mostly from his utility beft would come into play. Remember as we are dealing with a crossover, we have to assume that admantium would be somewhat attainable in both characters worlds, and Wayne Foundation would be a place that would be able to have access to it. As Martial artist Batman would have the edge, but due to Wolverine's sheer ferocity we'll just balance those out as even. For sheer fighting power Wolverine would win, but in a comic book match Batman would find some way either by invention of gadgets or his intellegence to subdue the canadian critter.
Anyway that's my take on it
apparently not the only ones take, I just found these from artist James Nguyen's site
