I think this show does hold up. Of course there are cheesy moments or bits of bad acting but that's part of the charm. It's not written for adults, but a lot of the stuff in there is above kid show material as well. There are stories about religion, bigotry, time travel and alternate futures, persecution, coming to terms with who you are... etc.
I've always heard that it was one of the first cartoons to do serialized storytelling - so you could get a 5-part Phoenix Saga, or a season-long arc where Beast was on trial so he could defend himself and mutant rights to the public - and that kind of stuff hadn't really been done in this medium.
You also get some great portrayals of the X-Men's rogues gallery - some of which improved upon and then influenced their comic counterparts. Apocalypse, Mister Sinister, Omega Red, Sabretooth.
IIRC: Season 1 is a Sentinels arc Season 2 is Mister Sinister and a bunch of hit-or-miss solo episodes focusing on each X-Man Season 3 is Phoenix and Dark Phoenix sagas Season 4 brings it all together with an awesome 4-episode Apocalypse finale
Sure, some of it is bad (specifically season 5, another studio tacked on a few more episodes, let's never talk about it), some of it is so-bad-it's-good (specifically Gambit's solo episode - incredible acting all around), but a lot of it is pretty damn great.
I never understood what was going on in that show, when it was on TV. I would have been 5-10, so maybe it was a bit over my head. I was more of a Batman the Animated Series kid.
I've always wondered if the rest of the team wondered how in the hell Jubilee made the A team cut. We have all of these super powerful folks....and then this teenager who can make her hands go sparkly.