Disclaimer: I've been to Akerhaus (breakfast), but not Park Fare.
Well, there are no princess for breakfast at Park Fare (it's Pooh, Tigger, Alice, and the Mad Hatter), and technically only one princess for dinner (Cinderella). So if you're in it for the princesses, Akerhaus is better on that score.
For food, Park Fare likely has a greater variety. Akerhaus has traditional Norwegian food for lunch and dinner, with a more basic breakfast. Park Frae is a pure buffet, whereas Akerhaus has a cold buffet and plated hot meals.
Akerhaus also includes the photo package with the meal credit.
On the whole, I'd say Akerhaus. Regardless of which you choose, have fun!