We've done and loved both, and will do both again. Some things to consider:
Transportation at ASM is much quicker. If getting little ones home quickly is important, you'll be better off here. FW has an internal bus system that you have to transfer to and ride once the park bus drops you off.
Your 16 year old may not care for the fold-outs at ASM. There is only one "real" bed, and everyone else sleeps on fold out chairs and sofas. My teen prefers the murphy bed at FW, plus she is not sleeping in hearing distance of her brothers there (they snore).
ASM has better theming at the pools and outside the rooms. More fun and more colorful.
FW is MUCH quieter! There are also more kids' activities there -- a petting zoo, a beach, walking trails, playgrounds, an evening campfire -- for those who plan to spend time at their resort.
FW has a kitchen. It's a nice -- and much cheaper! -- to eat breakfast in your cabin than at a crowded food court.
ASM has the advantage of 2 bathrooms. Lately, this has been the deciding factor for us, given a teen who takes 45 minutes to straighten her hair.
I think you'll be very happy either way. It's just a matter of what fits your family best.