Never cruised. Considering Disney. 3 kids 12, 10, 7

My family and I have never cruised before and are considering Disney, Carnival and RC. I have heard good things about all three. Although I'm sure Disney can't be beaten (who knows, maybe they can) when it comes to service, quality and cleanliness, I'm a little concerned about the appeal to my 12 year old daughter and 10 yr. old son. (My 7 year old son will be fine either way.) Both Carnival and RC seem to have so much to offer kids of all ages. Does Disney compare where activities are concerned or is it geared mostly to the younger kids? We're considering either a 7 day Eastern Caribbean or the 3 day land/4 day sea combo. Any comments would be helpful. Thanks!