Man, any problems the X-men have are like any of the same problems any other comic books have.
superhero comic books as a whole kinda "suck". Comic book writers are kinda foolish and as time goes on things just get more muddled. And you know who would probably agree with me? Other comic book writers. Interesting, neat storylines and one-off things occur but...that's all they are. Neat and finite. They aren't representative of the genre as a whole.
But yeah, this whole problem is especially true in terms of destruction level events (which lets be real, aren't actually worth that much in comic universes) is especially not that relevant for the X-Men since at the end of the day...they're still the X-Men. Their problems still exist are neither increased nor decreased.
The best X-Men stories have been about not necessarily the team, the fighting, weird conflicts, going to hell, magic bullshit but just the problems with being an straight up mutant. And handling storylines that deal with "Hey being a mutant is cool but also kind of a pain in the ass, not because of politics but because the line between superpower and disability is a thin one. Oh, and mutants can be assholes too."
"X-Factor Investigations" was interesting since it was sorta centered around James Madrox, Multiple Man, one of my favorite mutants. He's like the epitome of an average mutant. He has a simple but weird ability: He creates duplicates of himself. It has it's advantages and it's disadvantages. And it thoroughly explores that idea the fallout from such an ability. Aside from that, "Investigations" also handled more of the average street level mutants and how events such as "House of M" and "Decimation" were affecting people who weren't necessarily directly related to the central X-Men team.
But everyone has their favorite storylines for one reason or another and well, that's sorta the center of the issue, as a whole thing it's all a mess.