I assume by "day camp" you mean "kids facilities"?
I cannot compare to RCCL but I think Princess's kids facilities are better than Carnival and _much_ better than Holland America. On our recent Dawn Princess cruise, I found my three kids (ages 8, 14, 17) spending most of their available time there. Normally the 17-yr old would rather hang out with us, but he found their teen center very "age-appropriate". And they seemed to do very well with projects for the little one too.
Our group will have two 6.5 year old boys, one 5 year old boy and a 3.5 year old girl. Do you know if individual baby sitters are available in the evening from about 9 pm til when ever we get back to the rooms?
My experience is that Princess does not have individual babysitting in your room. They do have group babysitting in the the kids center that goes from 10 PM until 1 AM. You need to sign up for it and there is a charge.
There is no private sitters on Princess only group babysitting from 10pm-1am and this costs $5.00/hr/kid. This must be signed up for in advance like before noon that day.
You must also sign up a day in advance for port day service which is free, but if you do not sign up the day before they will not take your child (I have seen this really tick off parents who had a plan to shop in the morning in St. Thomas). (The better you understand how to work the system the better time you will have) If you decide not to use the service there is no charge, so my advise would be to sign up just in case and then tell them if you are not going to need them out of courtisy (each day brings new things and you never know). The kids crew get to leave the ship and have a day off if nobody is signed up.
RCCL and Carnival are always open on port days and no advance sign up is needed.
NCL also requires advance sign up as well and they charge if you are a no show.
Princess kids club vs. RCCL
Princess is more sedate, which is not always a bad thing. Take the 10-1am time frame
on RCCL the kids club is wild with games like gagga ball and, contests etc. on Princess it is quite time where they watch a movie with pillows and blankets. During regular hours they are about equal in activities. Same hours 9-12 2-5 and 7-10.
I think the group that has the least good experience on Princess is the 9-12 age group.
There does not seem to be a dedicated location for this age group on most ships and the activities compared to RCCL can be boring.
I will be on the Aug 25 Crown sailing and it will be interesting to see if they have expanded the program for this age group. My DD will be 12 and DS 8.
We have sailed Princess, Golden and Sun
Carnival Inspiration, Destiny, Glory, Victory and Triump
Just off the Diamond and I give Princess a big thumbs up for the kids zone. My girls are 11 and 6 and on the Diamond the 11 had a dedicated room that was quite large with great activities planned. Both my kids spent most of thier time at the fun zone we did not use after hours or port day supervision so I cannot comment. I think that for that difficult 10-12 year old group, the make or break factor, is wether they are able to make friends at the kids zone.