If one is used to the Celebrity Suite experience, then the Princess Suite experience will likely be disappointing. Following compares Celebrity's Sky Suite to the lowest suite on Princess:
1) Physical space: Princess wins here because their lowest level suite will be larger than SS (separate living room and bedroom, although the separation is a curtain).
2) Luminae wins hands down, in terms of ambiance, service level, and food. The Club Class restaurant is an extension of the MDR--food is meh in our experience, typical main dining room fare. Service in Club Class is better than MDR, but not to Luminae's level. But Princess' breakfast in Sabatini's for suite passengers is a good benefit.
3) Retreat lounge/sundeck on Edge class is the big winner here. No dedicated sundeck on Princess, and the lounge for suites on the Royal class ships is small and a bit claustrophobic (no window to the sea).
4) Celebrity's butlers if used are wonderful. No butlers on Princess. There is a concierge in the lounge, but the service is nothing like the over-the-top pampering that some butlers can provide.
5) Amenities offered by Princess not available with SS: Princess suites have first night specialty dining, one-time bar setup with mini liquor bottles and beers, unlimited laundry