I think in this fight, depending on location, Punisher should win this. If batman is in a vehicle then he has a huge advantage. If Punisher actually made use of the technology available out there today I think he could kick Batmans ass. Batman obviously has phenomenal reflexes and observation skills but a .50 sniper bullet from cover at about 1km should punch through a rubber/Kevlar suit like it wasn't even there. If they stood toe -to toe and just tried beating on each other then who knows. The punisher has been described as the ultimate human fighting machine. From the comics Punisher has taken on superpowered individuals and just won although he struggles with high mobility characters like Daredevil. From the TV series Punisher is slightly tougher than ordinary people but can take a huge beating.
Obviously Batman would cheat... It also depends which incarnation of punisher, the completely amoral psycho version, or the one with sort of a code of behaviour.
Thoughts..
Batman vs Punisher
Batman vs Punisher
Imagination is more important than knowledge. Knowledge is limited. Imagination circles the world. -Albert Einstein.