When we sailed on Royal Caribbean, several people said that they hated Carnival and would never travel on it. It was interesting to see that when we traveled on Carnival that we met people with the exact same dislike of Royal Caribbean.
Overall we liked both. We sailed on the Mariner of the Seas twice and the Carnival Liberty once. We liked the shows a little better on the Mariner, although, Carnival had great comedians that we really enjoyed.
We like the kids program on both ships. Royal Caribbean had a wonderful kids program. I would say that on our ship there were an equal amount of children. Some cruises definitely don't have that many kids. Usually the Caribbean cruises during the summer do. If you don't like children on board, travel during the school year when they are at school.
We would sail on either cruise line again.