I personally prefer Carnival, as I think the entertainment is better, and the price is absolutely better, but since you're traveling with kids, you might want to give RCI a shot. They do offer a lot of activities for the kids, like the rock wall, the ice rink on the Voyager class ships, etc. Carnival does have an excellent childrens program as well, and they do have the slide on most of the ships which the kids absolutely love. One other thing is the 24X7 ice cream and frozen yogurt. (a big plus in my opinion) You won't go wrong with either line, so look at the price, and the age of the ship etc, then make your choice.
Have a great cruise