I have sailed on the Caribbean Princess and on two Carnival ships (Valor and Holiday)
Carnival had better service, food, entertainment and was more fun. Carnival also does not nickle and dime you like Princess does, for say Ice Cream or juice!
Princess does have it's good points though. We loved the learn at sea program they had where you can learn to scuba dive, process photos on your computer, take dance classes and a number of different things. As you can see in my signature, we are taking another Princess cruise this coming December. If that cruise isn't better then the first we are going to mark them off of our cruise line list.