Having stayed at both, I can give you an informed opinion.
POP is great for many reasons that have already been listed.
1. Dedicated bus service - I can't stress the value of this enough. Plus, if there's a long wait for a POP bus, you can always jump on a AoA bus and take a short walk over to your room at POP - I believe it's somewhere around half a mile, which is equidistant to the walk from Space to Pirates.
2. POP is newer, although IIRC, ASM has been refurbed recently. But the last time I stayed there, it was clear ASM needed some TLC. Badly.
3. In my personal opinion, the food court is better, plus you can eat at Landscapes of Flavor at AoA which is very close by.
4. Large groups (e.g. football kids, teens, Brazilian tour groups, etc.) tend to stay at the All-Star resorts due to the lower price. Keep this in mind.
5. Dedicated. Bus. Service.