We've stayed in CBR and ASMovies - and enjoyed them both
CBR was out very first taste of a Disney resort and it spurred us on to always wanting to stay on-site to do the Disney parks in future (we stay off-site to do the non-Disney things). So, when we booked ASMo, we expected to notice that we'd 'downgraded' from a moderate to a value resort. In fact, we loved it just as much as CBR, but for different reasons.
CBR has slightly more luxurious furnishings and fittings in very slightly larger rooms, a slightly less 'cafeteria style' dining area, more exotic vegetation and landscaping, quiet pools as well as the themed main pool, and generally feels more removed from the hustle and bustle of the parks than AS.
AS has great Disney theming (very much in-your-face

), a good food-court and shop, good pools and transportation, as well as the same on-site perks as all on-site resorts, whatever their price range. It can feel noisy and busy and is more obviously child-centered than CBR.
I would certainly be happy to stay in AS again, and I'd probably only opt to pay a bit more and stay in CBR if I knew I was going to enjoy some time around the resort, and not just be sleeping there
