Hi Ivyandlace:
I've stayed at both resorts.
Our family of 6 stayed at the FW cabins summer of 2000 in a new cabin and really enjoyed the extra room. We saved $$$ and time by having breakfast in our rooms. They were very quiet and relaxing. If your family will be sticking close together, you may enjoy the "congregating" areas - the family room/ kitchen and deck. There is a bit more privacy here. The bath is full and there is a back bedroom. The "changing" area at the AS is the small tub/toilet area. There are a lot of other things to do at FW, too, if you feel like taking a break from the parks.
As far as theming - well, FW is "natural" - trees, trails, lakes,...ASMovies is "fun". Both pools are basically holes in the ground. No slides. ASMo's Mickey was neat around the pool. I guess AS pool was more festive.
The Trails End Buffet was pretty good and not too expensive by Disney standards. It had everything from pizza to ribs to veggies and salads. I do not recall a "food court" area. I guess they assume you will eat at your site.
Transportation at FW is more complicated. You must take 2 buses in order to get to most theme parks and FW is so huge, it has an internal bus. Check this out and consider renting a golf cart unless you plan on bringing bikes. This is $45/nite extra. On the flip side, we drove to all parks except MK and enjoyed driving up to our front door at nite.
A few other comments and opinions:
I felt cramped in AS room with DH and 2 small kids (under 4). Not much storage space.
We rented a golf cart and were glad we did.
If using Disney's transportation at FW, make sure everyone understands which buses to board. (My parents got lost!! Took an extra hour to get home).
We thought the pool was really crowded at FW. There are two pools - the cabins share their own aprtment sized pool. Disappointed here.
Really liked AS but too small for more than 3 days.
Staying at FW again in May for 8 nites.