As far as I can tell, _none_ of the Princess ships have water slides. But I bet that once your kids see the kids area, they'll be more than happy to go there. My youngest (now 8) is a serious mama's girl but she will gladly leave Mom for a cruise kids center. She's taken 5 cruises now (first when she was 3) and always spends all available time at the kids centers.
Don't worry about the kids on Princess. They have a really great time. We have traveled with our niece twice, (9 years old), and we always have trouble getting her away from the childrens activitys to join us for meals. She absolutely loves cruising, and especially Princess.
P.S. As far as I know, only slides are on Carnival.
The other thing about Princess versus lets say Carnival is that the pools are fresh water, something someone like myself appreciates and I am sure your little ones will too. There is also a lot more pool space on a Princess ship than say Carnival. Ok enough Carnival bashing for me for the night.