We've been to all three....castle and askershus many many times....park faire only once. We were not impressed with park faire, atmosphere or food.
Castle:
The castle is magical. You have to go at least once, and at age 7, she will still "believe". It's a great experience, and we have never been disappointed..afterall, you're IN THE CASTLE. You enter and wait in line to get your pic with Cinderella (included in the price), then you walk up a winding staircase to the dining room...which looks like a castle dining room, dark furniture, stained glass windows overlooking the park. My husband loves it, and no matter how tight the budget is, we go to the castle every trip. Try to get an early breakfast seating, get into the park before it opens, there is nothing like walking down an empty mainstreet. We have only done breakfast at the castle...never lunch or dinner.
Our experience characters at the castle were: Cindy (pic), Jasmine, Snow White, Aurora, Belle (blue dress) and Mary Poppins....we have been four times in three years and it has been the same.
Askershus (spelling??):
Askershus is quaint. We love it there too, but it is 2nd to the castle. I'm not fond of the lunch/dinner menu there, but we're not going for the food. My daughters call Askershus, Snow White's castle!!! We have done lunch and dinner there...we enjoyed both....
Both dinner and lunch have great character interaction....Lunch: we have experienced Ariel (with legs) at the picture area and then Belle (blue dress), Jasmine, Aurora, Cindy, Snow White walking around....and for Dinner we have seen Belle (yellow dress) at picture area and Jasmine, Aurora, Cindy, Snow White and Ariel (with legs) walking around.
Remember, Disney doesn't guarantee which princesses will be there....but it's usually the 4-5 main ones.
Breakfast works well for us because my girls are early risers, and you never know how tired/cranky you are by the end of the day for a sit down dinner.
I think that you will be happy with either one...but if I had one to chose, it would be the castle. My girls enjoy them both and it's a toss up for them....they love seeing Ariel with legs (I think it's because you never see her like that!).