If you're looking for babysitting, go with Royal Caribbean. THey have private, in room babysitters. On the other hand, Carnival only has group babysitting in the morning of port days and after 10 pm. at night.
Also, Royal Caribbean has interactive 45-minute play sessions for babies (6 to 36 months) and their caregivers, on a daily basis.
Let me know what you decide. (Royal Caribbean sails from Bayonne, NJ -- right near NYC).
Family Cruise Editor