Food: Celebrity wins here. The food on Princess reminded me of low end food service. The breakfast buffet in the Horizon was awful (same food served in the sitdown restaurant)in particular. The lunch buffet was mediocre, and while the presentation of dinner in the anytime dining Capri was nice, all the food tasted the same...bland, unimaginative, boring. As compared to the Star Princess, Celebrity was more flavorful and interesting. The breakfast in the sitdown area was more "highend" than the buffet on the Century. On both ships, the coffee was bitter and strong.
Tours: We like going on the tours offered by the ship...so stress free. Celebrity wins here. On the Century, the tours were a tad more organized. Paddles were provided for group recognition.
Entertainment: Celebrity again. The Century had better singer and dancers...the singers on the Star were a step above average. The Star also had a magician who was bordering on obnoxious. The venues on the Celebrity are better...larger venues to create energy. The Star had too many different bars/rooms which resulted in only a few passengers in each. Being a port intensive cruise with early calls, there was virtually no night life. At 10 pm, the ship was done. At least on the Century, there was music and dancing before dining.
Public areas: Varied. The Star's large screen "Movie under the Stars" was impressive. The World Cup was televised live. The decor of the Star is starting to look dated and none of the rooms have a wow factor. The Century had a specific martini bar with a bar constructed of ice.
Cabin: Again, Celebrity wins. Our cabin on the Star was a little "locker room" smelling. The Star had more hanging space.
Service: A draw. We were disappointed not being able to change our anytime dining to traditional even after talking to the matre'd immediately when he was available.
Activities: Princess wins here with lecturer John Lawrence and his port information. Sailing the Baltic for more than 19 years, he provides port information along with history. Both ships have similar activities...bingo, trivia, special "classes" on computers, cameras, etc.
Passengers: If you want a more high end fellow passenger, go with Celebrity. For example, on formal night we saw only 10 men in tuxes on the Star, while on the Century about half dressed black tie with the remaining men in dark suits. Very casual on the Star which may be a result of the anytime dining. On the Star, one half were American and there were 300 children on the ship.
Overall: Celebrity just feels more high-end and special. It's like comparing a Four Seasons to a Marriott.
I'm including Oslo here. You really don't need to spend $$$ on a tour. There's not much to see in the city of Oslo. Some passengers went to Vigland and they were disappointed. Shuttle buses to City Center (City Hall) available.