The AA is a "pull through" piston design (rod comes out through the front of the gas block), leaving nothing behind. The CMMG is also a "pull through", but leaves behind a spring tube which is attached to the gas block.
They both work similarly, but have slight differences. An AA requires a mil spec barrel nut due to it's piston rod spring cup (has to rest against the barrel nut). The CMMG does not require a mil spec barrel nut is more friendly with FF rails since it's piston rod spring is captured at the gas block end (that tube that's attached to the gas block). However, that spring tube may require opening up some FF rails ID's at the front end a bit.
The AA uses a cam type setup to retain it's "plug", where you just twist an pull out. The CMMG uses an "end cap" (a threaded screw/bolt that must be removed prior to pulling through).
They both use proprietary BCG's with everything else mil spec.
AA is MUCH more prevalent in the aftermarket sector, where as the CMMG is less so but is used (versions of) in factory rifles (Ruger, Stag both use CMMG variants). CMMG seems more interested in the factory level sales, and AA seems focused on the aftermarket level sales.
Both seem like great systems and you'd not go wrong with either one.