well, we have 2 Celebrity and 2 Princess trips in the last couple of years and would book either one again in a nano second. I always feel it is unfair to say any one line is "better" than another because so many things (well darn near everything) are subjective. Service, food, Entertainment, heck even the size of the shower.....what may be big to me is small to you or vice versa. So you ask, why Celebrity?
Celebrity does small things that make their service a little level above Princess. Some of these things have been mentioned, the greeting with the champagne and escorts to the cabin, cold towels or hot chocolate at the gangway when you return from shore trips and the one that I always loved was the smiley guy at the buffet entrance that always greeted your arrival with a hello and smile that led you to believe this guy had the best job in the world. The small item I enjoyed was on the Alaska trip. The lounge chairs had a very nice padding on them and the staff put out deck blankets on all of them, a very nice touch.
We were never bored, always found something to do and found the disco/night club to be hopping till last, every evening.
What would I like on Celebrity? The pools close early but the spa pool and hot tub are open late, I would like to see all of them close later. A self serve laundry would be nice but they do wash/cleaning for a reasonable price. The in-room entertainment could be increased a little, I think pay movies are on cruise ship are just wrong!.........but very few nit picky things. Celebrity is a very nice experience and truly not "stuffy" as some may think.