Well, it's sort of an easy call for me: Celebrity...no contest...
Of course, cruise lines tend to differ even internally ship to ship and itinerary to itinerary...
My comparison is based on my last two European cruises
August 2001 to the Baltic on the Crown Princess--10 nights
August 2003 to the Mediterranean on the Celebrity Millennium--13 nights
It may be a slighty unfair comparison in that the Crown was then an 11 year old 72,000 ton ship and the Millennium a 3 year old 91,000 ton ship, so you can take that into consideration...
However, being as subjective as possible...not only was it a "no contest" overall, the Celebrity cruise blew away the Princess cruise in EACH and EVERY category...
Obviously, the Celebrity ship was far nicer, more modern, in better condition...but it was also roomier, better designed and had far more amenities...
In addition:
Entertainment: Celebrity was "good" while Princess had the absolute worst entertainment of any cruise I've ever been on...Comedian was old, stale and generally not funny, xylophone player was the best show...The piano bar guy had more talent than all of the main showroom talent put together...and Princess had no late night shows...if fact, the whole ship was virtually "dark" by 11:00 each night...
Food: After all the build up, the food on Princess was average at best, Celebrity--better...
Service: Dining room staff was excellent on both, but the crew elsewhere on the ship on Princess was somewhere between unhelpful and nasty...Everyone on Celebrity went out of their way to be helpful...
Style: Princess was surprisingly tacky compared to the elegance and class of Celebrity..
Amenities: Blame it on the disparity in ships but Princess was lacking on everything beyond the basics...Celebrity had so much we didn't have the time to avail ourselves of all she had to offer...
Note on late night and extra food: Celebrity had a susshi bar with an extensive choice open 4 hours nightly, free ice cream every afternoon and Pizza available late into the night...Princess had none of this...and the pizza place closed down at 10 or 11 nightly...
In my book, there's no reason to cruise on Princess when you have Celebrity available...