We've stayed at ASMo, ASSp, and POP and there's really not a lot of difference. The rooms are exactly the same size, same amenities.
POP is MUCH bigger---translated meaning many more people. And the grounds are huge. It's fine if you're in one of the close buildings, but if you get stuck way in back, you'll have to pack a lunch just to head to the snack bar! We were lucky and got a close room in the 70s building and loved it. But I watched some of the other people hiking back and it didn't look fun.
Despite what some have said here, the *** do often have their own transportation, especially at busy times like early morning and park closing times. We found the wait and crowds with the buses about the same all around.
Pools are about the same at any of them, nice but basic. If you stay at AS, you can go check out the pools at the other two AS resorts as well.
It really is all about the theme. Talk to your kids and see what interests them. My guys loved being in the Toy Story area t ASMo, but then also liked the football bldg at sports. They didn't so much "get" some of the themes at POP--we had to explain what some of the things were!