the biggest difference you will physically notice is the decor and ambiance. There is no glitz-glamor or Las Vegasy type decor or feel to Princess. Its casual-elegant with more of a nice resort hotel feel to the ships.
You won't find as many families with infants and small children on Princess, if you go during school break you will find plenty of school-aged kids and teens. Princess limits the number of kids per voyage.
Princess pools are fresh water not salt and they are open pretty much 24/7 except for a couple of hours in the wee morning(or late night) for cleaning. Same goes for the hot tubs.
Princess offers Anytime Dining - which is exactly what the name says, you can dine at the time of your choice - these are main dining rooms.
You won't find any belly-flop, hairy chest contests, and no singing waiters on Princess.
Plenty of nightlife to choose from-- everything from nice quiet cozy bars with a band for easy listening & dancing, discos, show lounges with live music, production shows, comics, gambling, deck parties, and the Midnight Champagne Fountain (2nd formal night)- this is a must do.
A nice surprise on Princess - they have really good hot dogs, burgers and pizza by the pool.