Weaknesses

Unlike characters such as Superman, neither Batman or Wolverine has a specific weakness (like, say, Kryptonite), but the fact is they are both vulnerable to a number of different kinds of attack.
Both can simply be beaten down with crude physical attacks (such as punches), although it takes a lot more to put Wolverine down than it does Batman.
Both men are also susceptible to mind-control, magic, powerful energy attacks and pretty much any other type of offensive move if it’s of a high-enough level to bypass any durability or resistance they may have.
However, the fact remains that neither man has a specific weakness to speak of, so this particular round is relatively moot.
Winner: Tie.
