I'll try to answer a couple of things that you asked just from things I remember.
Most Carnival cabins are larger than Princess.
Princess has the Movies under the Stars on some ships, but not all, so it depends on which ship you are booked on.
Princess has fresh water pools and the pools and hot tubs are open late.
The buffet on Princess is open 24 hrs.
Lots of activities and shows on both lines.
I'm sure that others with a lot more experience will add to this. I adore Princess....it's probably my favorite cruiseline, but this year I'll be on Carnival for the new itinerary, so ready for a new adventure. My advice? Try them all at least once..they all have pros and cons...Happy sails....