I've been on both the Carnival Legend and the Mariner Of The Seas. Loved both of them, but each ship had strong and weak points.
The Mariner has more to offer for kids. The kid's area is huge, with the arcade and special rooms set aside for the youth programs.
Legend has a huge water slide - RCI doesn't do slides on their ships - but I'll have to tell you that slide on the Legend is not open often and can be affected by winds.
Carnival has the best pizza at sea....RCI pizza isn't even close! In fact, the pizza on Carnival ships rivals any land-based pizzeria in my opinion. Carnival also has great deli sandwiches, which is something RCI doesn't do.
Carnival and RCI are equal in the main dining room, although I think RCI is raising the bar and may be a bit better over the past year.
Bottom line - you can't lose with either ship as your choice. If it were me, I'd go with the Mariner because of all the "stuff" it has for kids to do.