I've stayed at both, and at the time I stayed at them I preferred All Star Movies. I liked the fact that the food court and the store were separate, I liked the theming better. Disney movie icons made it feel more like I was in Disney than the POP icons. However, and this is a big consideration, when POP was built, they took what they did at the All Stars and made it a little bit better. More food court choices. A nice lake to stroll around. Play fountains for the kids. Queues for the busses (since added at the All Stars) and actual toiletries in the bathroom (also now available at the All Stars).
POP busses go directly to the parks, the All Stars sometimes share busses. (I've never thought that it was a big deal like some others, though.) Perhaps the biggest thing right now: POP is about 4 and 1/2 years old, and some rooms are showing signs of wear and tear. BUT, All Star Movies is 9 years old and is in even more need of refurbishment.
Are you aware that the other 2 All Star resorts have both recently been completely refurbished? For that reason alone I would actually pick either one of them over both POP and ASMU. The new rooms at Music and Sports look very nice. If you go to one of those resorts' FAQ's you can see pictures of the newly refurbished rooms.
If I was booking a value, I'd pick one of them. But if you want either POP or Movies, I'd probably pick POP not because I like it better but because the rooms are much newer. When All Star Movies gets remodeled like the other All Stars, I believe it will be the value of choice for me once again.