We have been on Celebrity Millenium and Grand Princess this year with our kids (ages 6 yrs, 3 1/2 yrs and 18 months). Of course I can't make generalizations about a cruise line from 1 experience but I must say I thought Celebrity Millenium was far superior in every respect, including the kids program. On Celebrity Millenium they have revamped their kids program over the past 2 years-they actually hired someone from the Disney ship (whom we recognized having cruised on Disney the year before) to revamp the program.
What we preferred about Celebrity's kid program:
1. The counsellors were extremely energetic and fun. They really seemed to enjoy being with the kids. On Princess the staff did not seem nearly as friendly and in fact seemed less than enthusiastic.
2. The play area on Millenium had a climber/ball pit where the kids could run around and burn off some energy. On Princess they did not.. The activities on Celebrity seemed much more innovative and fun-ie dress up as pirates and search for treasure on the ship/talent show/carnival night. During the week they also filmed the kids and made a video which they played on the cabin TV.
3. I believe Celebrity had more kids dinners with the counsellors than Princess. On port days the Princess kids program did not run until 7pm-10pm. In small writing at the bottom it stated if you wanted to leave your kids with the Kids program during the day you had to sign up the night before and there would be "limited activities" for 3-6yr age group. In essence it sounded like they were not too keen on having kids stay in the program while in port. When we tried to sign our kids up during a port day they wanted to know the exact times we would be dropping them off/picking them up. Celebrity seemed a lot more flexible.
We also found that on Celebrity the cabin steward/waiters in dining room and buffet area were more friendly towards our kids. Kind of suprising as Celebrity recommends to tip half the adult amount for children whereas on Princess kids tip the same as adults. Overall, our experience on Celebrity was much more positive although we enjoyed both cruises.
if you choose the Grand Class ships of Princess i think that you and your kids will have a great time. If you go during school break there will be more kids aboard. I don't think you can go wrong with either Princess or Celebrity. Another good feature of Princess is the "Anytime Dining" - great option with kids.