We have stayed in all three and like them all. For convenience, we pick ASSp. For adults only, we pick AASMu. For kids or Disney animation buffs, we pick ASMo.
Both ASMu and ASMo have a min building where the food court and shopping are located. Buses are located out front. Then the rooms are in the 10 outbuildings. In ASMu the buildings are aligned more linearly so that the layout has many standard rooms further away from the amenities. Movies and Sports have a different layout that are more closely arranged around the main building. This layout means that fewer rooms have any distance from the amenities and that none of the furthest rooms are at distances that are difficult.
ASMo has the theme that appeals most to young children, I believe. That is important to some families. ASMu has the more 'adult' theme of the All Stars, IMO. If you book at ASMu i would suggest staying in a preferred room.
Often buses are not shared by the three AS's but when they are, as PP said, they usually go ASSp-ASMu-ASMo. So Sports gets the slight advantage on bus pick up/drop off.
If you go when rooms are freshly renovated, ASMo might be a really nice choice for the freshly renovated room.
Have fun choosing!