This was a first time cruise for our family, and on the whole, a better-than-expected experience for our group of skeptics. Our cabins (for 2) were small, but no worse than some European hotels I've been in. The ship was kept very, very clean, the rooms tidied twice a day, the crew seemingly everywhere with a smile.
The ship towered over its neighbors in the port, and its size was best appreciated at night. Three large dining rooms kept the flexible-time eating arrangements working well --- we never waited more than a few minutes for a table, if at all, and service was prompt. I can't imagine why anyone would go on a cruise where you are restricted to one of two fixed dining times, since on days where you are ashore, the early time would be tough to get ready for, while on at-sea days, there's not much point in dining very late.
Since I can't compare to other cruises, for those who are also first timers, what I can offer is a comparison to land-based resorts.
The food wasn't what you would get in a fine, small restaurant, but was better than what you get in a large, all inclusive resort. Choice was ample, both in the dining room and at the buffet (where we ate lunch most days). Food was a bit underspiced for my taste. Portion sizes are reasonable --- no one is trying to suff you (For those who want to, you can order seconds, but I'd rather have to do so than have it all put in front of me at once.) Avoid the weak coffee at the buffet --- there's much better at the coffee bar on the 7th floor.
At night, a big ship means multiple entertainment choices --- two shows going at once, several bars with live bands, and an impressive disco soaring above the aft decks. For those like me comparing a cruise to a land-based resort, the night time options were much better on the boat.
Service in the dining rooms, bars, etc. was far better than at a typical caribbean resort. The quality of the entertainment was also superior. (Dont miss James "the kid" --- a wild eyed comic magician, and Scott Wyler was also quite funny).
Daytime activities aren't quite as flexible as when you are at a resort --- you have to wait to get off (particularly on the two stops where the ship anchors offshore and tender boats are needed), and you don't really have time to take in any of the places you visit. You just do an activity (beach, snorkling, etc) then get back aboard. Good swimmers should try the drift snorkling off Cozumel -- they scare you by saying its for "experienced" snorklers, but its no huge challenge and a great excursion.
Its easier to meet people on a cruise than at a resort, and even kids have an easier time matching up with others, even if they turn their noses up at the organized events.
Add it all up, and the Grand princess was a pretty grand time. An easy vacation with everything looked after for you, even if it all has a Disneyland, corny, plastic sort of feel to it. You never really leave the US, you never absorb much local culture, but you do get a no hassle vacation with old fashioned service.
While I haven't been on other ships, I can't imagine what they might offer over this one that would make a difference.