The thing is Wolverine would still have an advantage having adamantium bones. He'd still be faster and stronger than Bruce also.
The only advantage Bruce would have are intelligence and a slight skill advantage, nothing that would turn the tide in his favor.
Still if the objective is to make your opponent submit rather than simply decapitate him then that's debateable, Bruce has tremoundous willpower and was one of the original candidates to become the Green Lantern when Abin Sur died. He also survived for days inside a maze in Court of Owls while injured.
