Obviously, everyone is going to have a different opinion on that question. Remember; what one person loves, another will hate.
Personally, after having been on all of those many times, my personal feeling is that I would rank those three in this order from best to worse; Princess, RCCL, then Carnival.
While I feel Princess has better food and is great for couples, I do feel RCCL has better amenities for children, so we tend to sell more of them for families than any of the others, but their food is not up to par with Princess. Of course, if you want cheap, then Carnival is tough to beat.
This is why we personally love Celebrity above all of them (especially their new Solstice-class ships), but then we're seniors (62) and when you look at what they offer for the price, they can't be beat.
As I said, everyone has opinions, so I know you'll encounter those who disagree with me on the subject.