One important difference between the two lines is the fact that Princess offers the choice of restaurant-style seating (which I believe they call "Anytime Dining") or traditional seating, whereas Celebrity only offers traditional seating. Anytime Dining means that you just show up in the dining room at whatever time you want and you can dine with whoever you choose. Traditional seating means you have a set dining time, will be served by the same wait staff every night, and be seated with the same assigned tablemates.
There are pros and cons to both seating arrangements. Anytime Dining will gives you more freedom. You will be able to plan your dining time around your activities. You could probably stay in port a little longer since you won't have to rush back to shower and change in time for dinner. You could meet new people every night if you wish or dine alone.
On the down side, not having the same tablemates every night may not give you the time needed to get to know your fellow cruisers and develop friendships with them. Also, one of the bonuses of having the same wait staff every night is that they get to know your likes and dislikes within the first couple of days and they can often anticipate what you want without you having to ask, which creates a higher level of service.
Sorry to be so long-winded but I don't know if you've ever cruised before so I thought I should explain everything just in case. Hope this helps you make your decision.