Is there any difference between Batman's Gotham City and Superman's Gotham City?What happens if they make a movie in which both appear together? Which city will they show? E.g. in Justice League.
Superman doesn't live in Gotham City.
Superman lives in Metropolis. It seems to be relatively near Gotham geographically (both appear to be in something like the New England area), but they're definitely different cities.
In fact, there's often tension when one hero works in the other hero's city, and that is likely to be a factor in any meeting they have. It's certainly been a regular point of contention in previous teamups, especially when it's just about the two of them and not about the whole Justice League.
Some visual representations may have the cities look similar, but generally Gotham is more brooding and gargoyle-infested, with a stoney Art Deco style (at least since the 1980s Batman film and subsequent Animated Series codified that look), while Metropolis has sleeker lines and is more "modern" with glass and steel (to reflect the "Man of Tomorrow" theme) rather than Gotham's ornate stone buildings carved with humanoid figures.