From everything I've seen and heard, Princess has one of the best programs at sea. The counselors are top-notch, with plenty of fun activities planned for the kids depending on age group. Usually, the 3 to 6 year olds are doing things separately from the 7 to 12 year olds. Sometimes if there are a lot of kids on board, they'll break the kids up into even smaller groups based on age.
I've heard many parents say they couldn't get their kids out of the kid's program (the Fun Zone) to go to dinner or off the ship for an excursion. They're having so much fun, they just don't want to leave.
The kids also seem to make friends really quickly on the cruise which is probably another reason they don't want to leave the Fun Zone.
Have a GREAT Cruise!