I remember a story from years ago, possibly from World's Finest, where through a plot contrivance Superman found himself looking after Gotham City for a few days while Batman patrolled Metropolis.

Both heroes discovered their unique skills and methods were next to useless against the crime in their counterpart's normal milieu.

It was a cool story; a nice reminder that Gotham and Metropolis are just as much characters in Batman and Superman's worlds as the people are.