Batman vs. Wolverine
The Fight is On
If the situation warranted such a conflict, could Batman or the Wolverine stand his ground and allow the other to perish?
These are hypothetical exercises. So, there is no real right or wrong. There are a plethora of variables that could decide the contest.
Initially I see Batman taking an early lead by being a member of the League of Shadows. However, his stealth would work less effectively against Wolverine who could make delicate variations in smell. In any event, I'm not sure Batman could deliver a debilitating blow especially given the fact that Wolverine is self-healing.
Batman, Used to working in the shadows might possibly toss a few grenades in the direction of Wolverine. Somehow I suspect that Wolverine would be aware of this threat and leap out of range, thus thwarting Batman's offensive.
Since Batman would figure out that there was not a way for him to subdue the Wolverine's stubborn efforts to assail, I believe he (Batman) would make an escape via his batmobile or one of his other gifted vehicles.
A line of argument might be that the Wolverine would not allow Batman to retreat, and I could envision this happening. However, the Wolverine could be made to cool down by a variety of gasses and other toxins let loose in the atmosphere.
The variables here are nearly endless. My line of thought goes like this: Since Batman could not defeat Wolverine outright, he'd have to re-think his options, and his best one would be retreat. Batman could escape, but, later, he'd have to think of an ingenious way of capturing the Wolverine.