Note: any Disney references I make are about the TV network of today. Not the old days nor the old movies. I love me some classic disney movies!
The difference between iCarly and Disney? The writers of iCarly (and probably other nick shows, though I only watch iCarly) did their research.
Disney is way too dumbed down. It takes its audience for mindless absorbent sponges, or in other words, idiots. Like there's always a moral of the story, no one says anything offensive and if they do, well DARN THEM TO HECK! < my point exactly. It's not real in the slightest. In real life, there isn't always a moral. Protagonists CAN be mean, there isn't always a happy ending. People do insult each other and *gasp* get away with it. The Disney that is supposedly for tweens/teens makes me want to puke. No tween is that stupid to buy into that. (I'm not saying their stupid for liking it, everyone's entitled to like what they want of course. I'm just saying, they don't drink the kool-aid. They know better.)
An another note, the acting is quite bad. I'm not sure if it's the writers' fault and the actors are doing the best they can with it or what, but whatever it is, it isn't working. Hannah Montana...the only person I was mildly impressed by was Emily Osment, and even then it could've been the writing (although I sincerely doubt it -- Emily's probably just good at comedy). I don't even think Miley is that bad of an actress in OTHER things. But in HM its horrible. Which again, makes me think it's more of a writing issue then an acting one. The only person I don't get annoyed by is Emily's character, so whether its the writers or actress doing a good job with her, kudos. It's the only redeeming quality I can see.
There's no hidden jokes for the adults to enjoy on HM. iCarly is filled to the brim with them. Makes it fun for those of us out of our kid stage 
Point is, iCarly feels real. The actors make it convincing and the writing is just right. When Carly laughs in amusement at Spencer doing something silly or Sam smirks and wittily insults Freddie: it feels real. It doesn't feel forced. Don't get me wrong, iCarly isn't actually REALISTIC, and that's not what I'm trying to say. Of course it's not, it's far from reality. However, you can feel like you're watching the characters interact, not watching actors reading through their lines.
Despite what I've said about actors (and I do wholeheartedly think that iCarly actors are better...though I could be biased), I think it really does come down to writing and directing. There are probably better actors on Disney than we think -- they just can't show it with the crappy material they get.
Not meant to insult any Disney fans, really. Just sharing my opinion. Everyone can like what they want to like
