You are right. Each is a totally different experience. Your children will have a wonderful experience on either. The Disney ships do not have casinos. They took the space that would normally be a casino and made it into a children's area called the Oceaneer Lab. The dining experience on Disney is unique in that you rotate dining rooms between the formal dining room, the Animator's palate, and the Parrot Jungle. The Parrot is like a tiki decor, the Animator's palate is decorated in black and white pictures of Disney movies. As you go through your courses the walls color in. On Disney there is a separate pool for children and adults. They have a movie theatre on Disney where they show Disney movies. Ofcourse on Disney you have the Disney characters running around, and they have times when they interact with the kids. There are other areas for the teens called the Loft and the Stack. The kids also have their own buffet line with their kind of food (pizza, chicken nuggets, Mac&cheese, etc)
The Freedom and Voyager class ships are also in a league of their own. The new Freedom has the H2O zone, the rock climbing, mini golf, the flow rider, ice skating. They have their parades down the Royal Promenade.
Both Disney and RCI have the activities for the children divided by age groups.
I would go talk with a cruise oriented Travel Agent that can go over all the differences. Hope this helps.