I have done both the Celebrity Apex and the Discovery Princess this year. They are both similar in terms of quality and demographics, and I would sail either cruise line depending on the cost for a similar cabin. Below are the areas I feel each line is better.
Princess
Better buffet. It is larger and has more options. The Princess buffet is open all day and the Celebrity buffet will close leaving you with limited dining options. Also, the Princess buffet is full service and the staff will take your drink order and deliver your food to you. On Celebrity, it was an ordeal to wait around for your omelets and get your drinks.
Better desserts. The included desserts at dinner is significantly better on Princess and rivals the specialty dinning desserts on Celebrity. The desserts at the International Café is free and offers great variety throughout the day. Celebrity offers a limited desert menu at the café. The Ice Cream on the Celebrity Apex was very bad and had large ice crystals.
Better service. Celebrity has great service, but I feel that Princess slightly edges them here. I am not sure if it has anything to do with the medallion, but the staff on Princess are always looking to make your day better.
Princess Medallion. You can order anything from anywhere, and it will be delivered to you. This makes a huge difference on your cruise in getting anything you want at any time. I was able to send requests to my room steward for wine glasses or extra hangers.
Self service laundry. If you are taking a longer trip, going to the beach, or having pool days, this is a life saver.
Closet in room. I love the walk in closet and you should be able to hang all of your cloths no problem.
Cheaper specialty restaurants.
Celebrity
Better ships. I like the design of Celebrity over Princess and their dinning rooms are more inventive. Also the viewing angles on Celebrity are significantly better than the newer Princess ships. Princess really failed in creating any good viewing areas that is not an up charge. There are a ton of great viewing areas on a Celebrity ship if you are doing a sight seeing cruise. Also, the Celebrity ship has a covered pool and the newer Princess ships don't have a solarium. If the outside weather isn't ideal on a Princess ship, you can expect the indoor spaces to be crowded.
Bathroom in room. Does not have a shower curtain. Everyone hates the shower curtain on Princess.
Better main dinning room. I love that there are 4 main dinning rooms with different menus. This made dinner exciting every night knowing that we are eating in a new venue. The food quality I felt was just as good as Princess for the standard main dinning room.
Better drinks. Celebrity has a great variety of included drinks that you can access throughout the day. Also, the free coffee is great on Celebrity and the free coffee on Princess is a major let down.
Focus on rest and relaxation. The solarium is amazing and is included in your cruise fare. You have to pay for a similar experience on Princess and it is outdoors.
