Let's take the protagonists. X2 has Wolverine, First Class has Erik Lehnsherr (Magneto). Both have compelling missions - Wolverine's is to find the truth about his past, and Erik's is to seek revenge on the man who murdered his mother. Wolverine's mission is carefully developed throughout the entire movie, going from investigation at Alkali Lake, to interrogation of Xavier back at the mansion, to full-circle return to Alkali.
This is interrupted by William Stryker's attack on the mansion. But the two key points here are that a) the interruption is caused by the man who holds the key to Wolverine's mission, and b) Wolverine is forced to take this trip away from his primary mission - "I'll be fine," he tells Rogue as they flee the mansion. "But we won't," comes the reply. Wolverine must leave his mission in order to save lives.
In First Class, Erik's mission is interrupted by Sebastian Shaw (ok, good - he holds the key to his primary mission). But in contrast, Erik doesn't have to further divert from his goal of revenge. We've already seen that he is more than capable of fighting his way to Shaw and coming within spitting distance of him. But presented with the possibility of creating a cool team of superheroes with a guy he's just met, he says yes. Why would he do this when he can just fight his way back to Shaw and have another crack at him? This is a man who has spent his entire life filled with anger and revenge, and he's suddenly willing to put that on hold to mentor a few spotty teenage mutants? Sorry, I don't buy it!
The other problem is that First Class does a rather poor job of juggling a few too many characters. Our focus is on Erik for the first act (and what a great first act it is!), with secondary thoughts on Charles and Raven. Then suddenly we're expected to care about a bunch of teenagers who we haven't seen before. That's where the problem lies - we put a lot of time and effort into following Erik's story, but then we're cheated when the film changes from a revenge thriller to a motivational teen movie. And why should we care about them? For example, why was Alex Summers in prison? Why should I care about him if you won't give me a reason?!
In contrast, X2 juggles a large number of characters near-perfectly. Nightcrawler demands a bit of our time, especially later on in the movie where his knowledge and skills become vital. But it's ok, because he is introduced in the opening act. The same goes for Rogue, Bobby and Pyro. But again, we see them early on, so their stories don't come out of the blue. And their backstories are explained enough for us to care.
The only issue I have with X2 (and all of the X-Men movies for that matter) is that Cyclops is criminally under-used. Once he's kidnapped, we don't see him again until the finale, where he does sod all. But perhaps that was wise, as trying to deal with too many main characters can be a disaster (as First Class demonstrates).
Don't get me wrong - I like First Class (it's miles better than The Last Stand, anyway!). I think the first act is excellent, but it's downhill from then on. But X2 beats it on every level. Especially in the final act. Characters ring true in X2 (Magneto betrays his new team members, tricking Xavier into attacking every human on the planet). Whereas First Class expects us to believe that Raven is going to abandon Charles (a man she has spent the best part of her life with) when he has just been shot and paralysed (and may be dying!) in favour of the guy who just caused said paralysis and is wearing the helmet of a Nazi-friendly murderer!
Nah, X2 will always be far superior to First Class.