We've been regular cruisers with Carnival for 20 years, and have only once cruised with RCCL - a Mediterranean cruise from Barcelona on one of their smaller, older ships, The Vision.
We got a great deal in an Ocean View cabin with free wifi thrown in, and had a lovely cruise, with a fantastic itinerary, including a wonderful overnight stay in Venice, and several ports we'd never visited, like Split, Kotor and Villefranche, all of which we loved. In terms of value, we felt it was as good as we are used to with Carnival, which was surprising, as generally we find RCCL's prices far higher.
I agree with a lot of the points already made. The food and entertainment are better on Carnival. We were amazed at how quiet the ship was after about 10pm, and we really missed the atmosphere we've always enjoyed on our Carnival cruises. The service on board was fine, but overall I find the Carnival crew more attentive and friendly.