Adamantium claws and healing factor overcome Batman's superior tactics — you can't strategize against unkillable.
Batman is the better tactical fighter — his combat skill, gadgets, and strategic mind would let him control the early exchanges. But Wolverine's healing factor and adamantium claws present the same problem as Deadpool: you can't permanently defeat what won't stay down.
Batman's utility belt has answers for many threats — EMP, sonic weapons, gas. But Wolverine's healing factor shrugs off toxins and gas, his adamantium skeleton is immune to EMP, and his berserker rage makes sonic disorientation a temporary measure.
The key difference from Batman vs. Deadpool: Wolverine is a significantly better close-combat fighter than Deadpool. His berserker instinct and adamantium claws make him lethal at close range in a way that even Batman's martial arts mastery can't fully counter.
Without specific knowledge of Wolverine's abilities, Batman loses. With prep, he could develop carbonadium weapons (Wolverine's specific weakness) or electromagnetic restraints for the adamantium skeleton.
Batman is the superior tactical fighter with more diverse gadgets. EMP could theoretically interact with the adamantium skeleton. Gas and toxins might temporarily slow the healing factor. With prep, Batman could develop specific anti-Wolverine countermeasures.
Adamantium claws cut through Batman's armor and gadgets. Healing factor negates all non-lethal damage. Wolverine's centuries of combat experience and berserker rage make him relentless. One clean claw strike could be fatal for Bruce.
Wolverine wins through healing factor attrition and adamantium lethality. Batman is the smarter fighter, but Logan's combination of unkillability and unstoppable claws is a problem Bruce can't solve in a random encounter.
Batman also fights
Wolverine also fights