We've cruised mostly with Princess because of their itineraries and packages and have only done one Celebrity cruise. But that one on the Constellation was head and shoulders above what we've ever experienced on Princess. Celebrity is just a much classier operation - at least for that ship. Food and service was close but a tad better on Celebrity. Their prizes and how they conducted contests was better. For example, the not so newly wed game was done more professionally with the contestants getting a video tape of the show and nice prizes. The winners got comped at their specialty restuarant which was worth $50 plus receiving a garment bag, shirts and other paraphenalia. On Princess the winners get a bag or pen or key chain. Celebrity sends out preprinted luggage tags with your name and cabin numbers on them while you have to hand letter your tags for Princess. These are all little items but they are why I give Celebrity the edge and say they do it with more class.
So you have to ask, why don't I cruise with them more. I would if the right packages in the right places were there. I just did a Panama Canal on the Coral Princess but that was a special deal with my friends and neighbors from our community. Otherwise I probably wouldn't have considered it as we had done the canal before. They don't do the South Pacific or Australia. They are concentrated in Europe. They do some Alaska, Panama Canal and Mexican Riviera but I've done each of those at least 2 or 3 times. But when I start to retrace my voyages, they will get the first look in the future. I have to finish my 18 day cruise for SF to Papeette and my 14 day NZ-Austraila first though.
That being said, I can't vouch that their service in the Alaska, Mexico, Panama Canal will be as good as we experienced on the Constellation because that is Celebrity's flag ship. But for that one voyage, it sure stood out over my many Princess experiences.
My wife and I haven't been on Celebrity and are scehduled for our first Princess cruise next on the Golden Princess in Mediterranean. But we have been on HAL several times (2 on the Noordam, 2 on the Veendam, 1 each on the Zaandam and Westerdam). We have also been on RCL and Costa.
I can tell you that we have always enjoyed our HAL cruises but that the average age of the passengers will be much older than the other cruise lines. I would guess the lowest average age we ever had for a cruise was in the late 50's to early 60's. This can be both an advantage and a disadvantage. We were on one cruise and when we stopped at Half Moon Cay, HAL's private island, and I would guess less than a couple of hundred people got off the ship in spite of it being a great day for the beach. It was like having a private beach in the Caribbean. On the more active shore excusions you can often decide to sign up at the last minute and still get on. A disadvantage is the food, while being good, sometimes isn't seasoned as highly as you might want. Also some of the shipboard activities tend to be more oriented towards an older crowd. This is also true with the entertainment and music played in the bars.
I will be able to give you more information comparing Princess and HAL after our cruise. We return the first of August.