Abby,
Both are good choices for a dining princess encounter, so in the end you know that you are good with either restaurant.
As for how I compare them:
COST: Cinderella's Royal Table is notably more expensive, to the tune of at least $10 per person.
FOOD: I think the food is, on average, better at Cinderella's Royal Table. But I have never had something bad at either in recent years. I actually think that the buffet style at breakfast at Akershus is a bit more to my preference, but really the food edge overall goes to Cinderella's Royal Table.
CHARACTERS: While ANY character experience at Walt Disney World reserves the right to change the cast of appearances, Cinderella's Royal Table is pretty much the same all the time. Akershus has a bit more variety, and is more likely to include some of the lesser known princesses from time to time, like a family favorite, Mulan.
INTERACTION: I actually give the edge here to
Akershus Royal Banquet Hall, since they have a bit more than just the table-side meet-and-greet.
BOTTOM LINE: Because Ariel has a particular appeal for your daughter, and she is more of a 'guaranteed' experience at Cinderella's Royal Table, I think that is your better choice. Yes there is an added cost. But the overall experience, and greater likelihood of Ariel being there makes this an easy call. Also, if you have a choice, I prefer dinner there to breakfast or lunch.
Write me back if you have any follow-up questions!
Have a magical (and delicious) vacation!