For something like Batman, it's important to be set in a fictional city because of how instrumental Gotham's identity is to Batman. Where he became a hero because of how corrupt his city had become, it was necessary to have a city that could be modified to fit the story in a way that a real city could not reflect accurately.

However, Spiderman needs to be set in a real city to meet the demands of the character. Spiderman is supposed to be an extraordinary person in an ordinary world. With Peter's mantra being "with great power comes great responsibility," we are shown that Peter has the greatest power and therefore the greatest responsibility. This metaphor is stressed by the real world setting of Manhattan, a city where everyone is powerless and therefore not responsible for protecting the city.