Hi Mallory,
Both of the resorts that you are considering -
Disney's Art of Animation Resort and
Disney's Animal Kingdom Lodge - are magical in their own ways. Let me tell you what I like about each.
Disney's Art of Animation Resort is whimsical and fun. The animated themes of each area are larger than life. Your young princess will probably really enjoy the Big Blue Pool, which features a zero-depth entry and underwater music! There is also the Schoolyard Sprayground water play area for the littlest ones, as well as Squirt's Righteous Reef playground. There are other pools throughout this resort as well.
Disney's Animal Kingdom Lodge is immense and grand. From the soaring lobby to the broad savannas, this resort is unique. There are exotic animals to be seen around every turn, and there are plentiful activities on a daily basis, including many cultural programs focusing on Africa. The art found throughout the resort is amazing. Disney's Animal Kingdom Lodge of course also has a well-themed pool, Uzima Pool, with lush surroundings.
You mentioned "bang for our buck" as an important factor in your decision. Since Disney's Art of Animation Resort is a Value Resort and Disney's Animal Kingdom Lodge is a Deluxe Resort, you will almost always pay less per night at Disney's Art of Animation Resort. At Disney's Art of Animation Resort, you also have the choice between a standard hotel room and a family suite. For a family your size, you can save even more money by staying in a standard hotel room.
I am sure that you will have a wonderful vacation no matter which resort you choose, Mallory! Please do not hesitate to ask if you have any further questions.