We've sailed on the Zaandam, Mercury, and Norwegian Sky and all 3 had terrific kids programs. Activities were seperated by age. My son who was 7-8-9 on the trips enjoyed them a lot and I could see that the younger kids were enjoying themselves as well.
Parents had to sign the little ones in and out of the kids rooms so you shouldn't have to worry about security either.
I would guess that Princess and RCCL are equally good.