We like both lines but there are some differences. These are just our opinion:
The Royal ships themselves are usually gorgeous and better looking than Celebrity ships.
The food on Celebrity (generally) is better than Royal, particularly MDR and below. If you mostly dine in specialty restaurants or stay in a suite that gives you access to an alt MDR, you probably wont see a difference.
The entertainment on Royal is significantly better - both quality and quantity. We often skip the shows on Celebrity.
Celebrity is a much quieter experience, which is both a pro or con depending on your preferences. A pro is definately the casino - if you like to play the tables or slots, you will have an easier time finding a seat on Celebrity after 10pm.
As mentioned throughout this thread, you wont find as many children/minors on Celebrity, which is a definate plus for us.
Celebrity has an Aqua Class concept that gives you access to a healthier dining dinner option and access to the spa thermal suites, which is very nice.
I dont think there is a significant difference in service. We havent had poor service on any cruse.