Both Celebrity and Princess are quality "premium" cruise lines, so each offers an "upscale" product. I understand that the decor aboard Celebrity vessels tends more toward "California Modern" whereas the decor aboard Princess vessels tends more toward "Old World Tradiational" (except, of course, in spaces such as the casino and the disco) but this is mostly a matter of personal preference. MV Grand Princess is a much larger vessel than MV Mercury, but Princess has opted to provide more smaller spaces rather than simply making the existing spaces larger. Many of the spaces aboard MV Grand Princess actually feel intimate rather than overwhelming and there are more choices of activities -- including a choice of three different main shows each evening. Likewise, MV Grand Princess has three main dining rooms (named for famous artists whose works are reproduced in their respective murals) that are terraced and subdivided by partitions of wood and etched glass into small, relatively intimate areas. When you sit down to dinner, it really does not feel like you are in a room with about five hundred other passengers!
Each line has its relative strengths. Most published reviews credit Celebrity with the best cuisine and Princess with the strongest program of shore excursions, but I don't hear many passengers complaining that the other line is seriously deficient in either area.
The other significant new feature of MV Grand Princess is the alternative specialty restaurants, named Sabatini's and The Painted Desert. If you want to try them, I recommend doing so for lunch rather than for dinner. These two restaurants require advance reservations and a cover charge ($3.50 per person if I remember correctly) which goes to the servers in lieu of gratuities.
You didn't say which itinerary you have. If it's the "Grand Mediterranean" itinerary, you might want to check my post about the ports of call on the "Eurpoe" board. If it's the trans-Atlantic itinerary, some of that information would remain relevant.
Do have a great cruise!