We sail on both lines frequently and find that they are more alike than different. There are pros and cons to both and I can't say that I have a clear favorite, the decision is usually based on itinerary.
in my opinion, Celebrity has significantly better food and we love that there is no smoking anywhere inside the ship, including the casino. Smoking in the casino is the biggest negative to sailing with Princess for me.
On Princess, we like the fact that there is savory food available in the International Cafe rather than just the pastries and desserts available in Cafe al Bacio on Celebrity. We also like that availability of self-serve laundry on Princess ships. It makes a big difference on long trips. We also enjoy formal nights. We also like that option to order from the Medallion app on Princess ships, it's especially convenient for coffee in the morning and enjoy formal nights.