I've been on 3 - all a while ago, and all to the carribean, but on 3 different lines. I don't remember much, but here's what I can recall.
Celebrity: This was my favorite (it was my 1st honeymoon), the food was better, and they really catered to a luxury vs. "party" atmosphere.
Carnival: The food wasn't nearly as good (but edible), and just not as "nice" as Celebrity. Definitely caters to the party crowd more than the "high class" crowd. Still had a great time though!
Royal Carribean: this was somewhere in between the two.
I'd go on any of them again, but it would probably depend on WHY I am going - since I usually tend towards the "luxury" option I'd probably do Celebrity or RC again before I did Carnival.