The Batman-Wolverine fight has been debated and is an interesting one.
Wolverine's claws would cut through Batman's kevlar. Batman could not hurt Wolverine or break his bones.
But. Batman doesn't have to fight direct, his strategy always out manoeuvres his opponent.
I am not sure exactly how Batman would do it, and I would love to see it in a comic, but I believe he would find the strategy to defeat Wolverine
- he beat Superman FFS!