I have cruised Princess and Carnival both many times and found them to be very comparable in most areas. The one thing that I really liked better on Princess was the Anytime dining option and the more extensive dinner buffet. The 24-hour, fresh water pools on Princess are also really nice if you like to swim. However, I did miss the always available free ice cream that Carnival offers. On Princess, ice cream is only free for a one hour period each afternoon and at dinner. At other times, you have to pay for it.
Other than those things mentioned above, I found them to be extremely similar. My future cruises will probably be on Princess only because I really like the Anytime dining option, however if Carnival was to ever offer a similar option, I would book them again without hesitation.