Having done both several times, myself and my girls much prefer Akershus breakfast.
The only reason the Castle is better at all is the atmosphere/location. That's it, IMHO. Oh and maybe that for that rediculously high price you get the photo package for 'free'. Wow.
The Akershus breakfast's food is better, IMHO. (lunch and dinner, I do think CRT's food is better but we'd still go to Akershus!)
The Akershus breakfast is cheaper.
CRT is pre-paid or two Table service credits.
The Akershus breakfast, IMHO, has more princesses and you can see either Belle in her yellow gown as the greeter, and sometimes Ariel with legs, but she is usually scheduled for lunch and dinner. Sometimes even Cinderella is there. We got to see Cinderella there once. We've also seen Ariel, Sleeping Beauty, Snow White, Jasmine and Mulan. Sometimes also Alice and Mary Poppins.
At CRT, we've seen Cinderella, Belle, Snow White, Prince Charming, Fairy Godmother and sometimes Sleeping Beauty. Once a few years ago we saw Alice and another time Mary Poppins.