Think about it. Punisher works out of New York City, a very big important place in the Marvel Universe where many heroes, superhero teams, and villains reside and operate. It has been the epicenter of many wars and invasions. Punisher sticks to the street level due to his personal war, doesn't get involved with the bigger stuff unless asked- he stays in his lane so to speak.
Batman works out of Gotham where pretty much all incidents are at the street level. He is on an endless crusade to clean up the city, with limited success.
Put Batman in NYC for a month and at best he'd help in taking guys like Kingpin down. He might team up with Avengers or Fantastic Four if needed, but he isn't gonna do a damn thing to help clean up the city in a month alone- way too much going on in NYC.
Put Punisher in Gotham for a month and he'll murder the Joker, Penguin, Black Mask, Hush, Two Face, Riddler, Bane, etc. in a matter of days. He'll let himself get caught and put into Arkham Asylum, and he'll continue his mission to take out whoever is in there.
Put both men back in their homes after a month, Punisher will feel some sense of relief because he at least managed to clean one city up. He'll be inspired to take his war to the next level.
Batman however, will come back to a clean Gotham city. He will have become obsolete and he will fall into an existential crisis.
The best he could do is head over to Bludhaven and clean up after Nightwing.
@toasty need your input here
