But... Batman and Wolverine are different companies, thus different universes. Batman wouldn't know about Wolverine, unless of course there's been a crossover since the last re-vamp.
It wouldn't matter anyway, though. Wolvie might win the first battle, but if he lets Batman walk away to fight another day, he'll just create some adamantium-melting ray gun for the next time.

I'm sorry, Batman killed Predator. He has the knowledge and know abouts on every JLA member and can destroy them all with his plans. It will take batman all but five minutes in a fight to figure out what wolvie's deal is and kick his ass.

besides, Batman is a scientist.

and science rules!

Wolverine. Uh, a healing factor kinda nails it for me.

Batman would probably whup his ass for quite some time, but all Logan needs to do is land ONE claw, and human Bruce is toast.

Oh, and to paraphrase a rule from another forum:

Batman and Dr. Doom could beat anyone with enough prep time.

Holy crap. Are you FN shittin' me?

Every time, EVERY time Bats and Supes have ever fought, Batman has kicked his ass. Give me a break, man. Even in Red Son, the commie Bruce defeats Stalin Supes.

Sorry, but science can't combat healing factors, people.