I would say that Spiderman has nothing to prove to the world: he does what he feels he has to do.
He may be hated, he may be loved… he has faced all reactions along the years, it didn't change him. Well, the authors can't really change him. The readers love him for being first and foremost Peter Parker who hides his identity behind a mask and fights for justice. Peter Parker isn't usually at odds for being Spider-man, he is at odds for doing Spider-man's work.
On the other hand, X-men went through an evolution, they are more an author's creatures, more or less heroic, more or less moody, more or less sympathetic.
It depends on what the author wants to say.