facepalm I hope the Wolvie Brigade appreciates this...
Wolverine is actually pretty skilled in his own right. While he does have his moments of beserker rage and fighting like a crude animal, he knows various martial arts and how best to execute them. I don't know how you can honestly say Wolverine isn't skilled.
Furthermore, Logan is across the board physically superior to Batman in my books. There's not a strength or speed feat that Bruce has under his belt that Logan couldn't replicate or exceed.
I don't know what Batman is going to deduce here fighting a guy with exceptional skill, physical attributes equal or better than his, an indestructible skeleton with retractable claws, and a healing factor that could keep him fighting almost indefinitely.
Unless we're going with "Batman wins because he'll find a way...somehow".