Hi, Jennifer!
So you have already answered your question in the best way possible: stay at both!!
Frankly, the two Resorts are so different from one another that if you can do a few nights at each, you'll have a duo of incredible experiences.
Animal Kingdom Lodge is themed to make its Guests feel like they are in Africa, complete with animals, optional safari adventures, and perfect architecture.
Wilderness Lodge is a gorgeous ski lodge on a grand and glorious scale, modeled after the famous Old Faithful Inn in Yellowstone. Again, details make Guests feel immersed in the beautiful comfort of a rustic (and luxurious inn).
Service at these two Resorts is impeccable, as you would imagine, and each one offers a gorgeous pool, activities for families, and a kids' clubhouse with expert childcare workers that parents can use for a well-deserved night out (a fee will apply). The list of amenities at each Resort is comprehensive and really geared towards serving Guests of all ages.
And Disney makes it easy for you to try both Resorts, by offering complimentary luggage transfers; just let Bell Services know the night before you change Resorts, and you will be able to coordinate convenient arrangements with the Bell Desk.
I hope that didn't complicate matters
too much, but since you threw out the offer ... my vote is to definitely double-dip!
See you later, celebrator,
-Deborah B.