We took our DD on her first cruise at almost 4. She was great. Loved everything. We have only done Carnival. Had no trouble. The kids camp was great! We were on the Fascination. As it is an older ship, the rooms were "cozy". We are booked in November on the Pride with our DD and DS (he will be just shy of 3). Looking forward to "seeing" the cruise through their eyes
Personally, unless you found a super deal with Disney, I wouldn't even consider them. Of course, the prices may have come down since I looked when taking DD last year. Carnival is great for kids and I don't see why people talk of Carnival as the party line. Yes during spring break you have lots of college kids but over all, a great time!
Best of luck!!!