We have been to both a few times and they are completely different experiences. So it really depends on what your are looking for.
We loved 1900 we ate there for breakfast and dinner.
1900 Breakfast: we saw Alice, Mad Hatter, Mary Poppins, Tigger, and Pooh. The food was the best breakfast buffet we have had at Disney. Wonderful variety and high quality.
1900 Dinner: we saw Cinderella, Prince Charming, Lady Tremain, Drizella, and Anastasia. The royal family is an absolute hoot! We had a ball and laughed our heads off! The food was good, the coq au vin, was the best I have ever had.
Alkershus Breakfast: we've seen a few different princess combinations here Ariel, Belle, Snow White, Pocahontus, Jasmine, Sleeping Beauty, even Mulan the only princess we have not seen there is Cinderella. The food is good.
Alkershus Lunch: same princesses as above, but we did not care for the food. The only good food at the meal was the cold appetizer selections. Some of my family didn't eat their food at all. The desserts were bad also.
If you are looking for a straight up princess meal, breakfast at Alkershus is a good choice. If you are looking for an entertaining character meal then 1900 for dinner is a good choice.