Huh, this is a tough one, but I think I ultimately have to give it to Batman. They are both very, *very* dated movies, that proceeded to have significant influence on future works ( not all that influence being positive ). However, in the end, Batman has the edge for two reasons:
1. It has a very obvious major positive influence, in Batman: The Animated Series, and the ensuing collective works of Timm and Dini. X-Men really doesn't have anything that can compare.
2. Batman was a major cultural influence, standing on its own. X-Men was influential, but part of a broader moment in cinema, being preceeded by Blade and followed by Spider-man. It contributed to the Movie Superhero, but it didn't do it solo in the way Batman 89 did.