To my knowledge, Princess is the only line that uses freshwater pools ...
In my experience, the pools can be pretty crowded particularly on sea days with nice weather. They also aren't olympics sized so it's more for splashing around then swimming. Still, if your son is a fan, bring a couple of suits so you'll always have one dry.
RCI Sovereign of the Seas 2005
Caribbean Princess 2005
Carnival Paradise 2004