I take back my last comment,cause I thought about this a little more.....
IF Wolverine were to catch Batman off guard......something that RARELY happens to Batman.....I think Wolvie could slice him in half with little effort.
Otherwise,I doubt Batman would let him get the advantage.
When I said that "Wolverine is driven by rage,and Batman could,as said,exploit that and use it against Wolvie.",I meant Batman could realise that(Unless Ive missed something,Wolverine can get angry pretty easily.....but then again,I havent read much Wolverine latley.
),and exploit it,purposely making Wolverine angrier and angrier,with taunts,and cheap shots.Maybe,if he knew something about Wolverine,hit a nerve.
Wolverine would keep his cool and fight Batman,but if he allowed Batman to live long enough,eventually Batman would send him into a HUGE rage,making Logan lose focus.He'd slip up,and Batman would take advantage of it,by knocking him out with a blow to the head.
Of course,Batman wouldn't be able to kill him,or defeat him another way other than knocking him out,cause,as said,Wolverine has the healing factor.
So Batman would win,in a way....
A fight to the death,however,I can see Wolverine winning.
So,to tell you the truth,I can see a way for either hero to win,but it really depends on the circumstances.