We've stayed at POR a few times and it is an amazing resort. We haven't stayed at AoA but have visited there and have stayed at Pop Century a few times as well. To me, AoA felt very much like Pop. Great resort, but can get pretty loud. You're debating between two VERY different resorts, and I think it is going to take you deciding what type of experience you want.
If you want full immersion in the Disney experience, your suite at AoA will give you that, along with the big statues and theming across the resort grounds.
If you want a resort that's more laid back, has a bit of a more upscale feel, then POR is definitely worth a look. The grounds of this resort are beautiful. And even though it's not as kid-like, it is still very, very kid friendly. The pool is beautiful and there's a hot tub. They have a campfire at night where you can roast marshmallows. You can take the boat to DTD. You can take the kids pole fishing.
We had always stayed at the value resorts, but once we stayed at POR we were hooked!