Is there a benefit to midlength over carbine for function?

Any input on the two is greatly appreciated.

the difference between Mid and Carbine is not specific to any brand of rifles or uppers. there are two major differences.

the first is personal preference/future plans for the upper. a carbine has a shorter hand guard, so where you prefer to hold the weapon is the deciding factor. a mid hand guard is 2 inches longer than a carbine hand guard. with an AA upper that also limits the rail length you can use in the future. the longest carbine rail you can use is a 7 inch rail with a gas block cut out (9+inches total) and a mid will be a 9 inch rail with a gas block cutout (11 inches total)

the functional difference is the felt recoil impulse. the longer the gas system, the more gas will be burnt off, and the softer the felt recoil impulse will be. rifle is softer than mid, is softer than carbine, is softer than pistol.

I was thinking function specific to the AA piston uppers. I have a handful of both GI carbine and midlength systems, and know the personal preference for ergos, control, etc - just not piston functionality.

Would there really be more distance for gas to be burnt off in the midlength piston upper? I would think the piston rod would be longer, and the exhaust point not be changed (in distance from the gas block)

No. There is no benefit other than longer handguard. In a DI system, the length of gas tube affects the "pulse/timing" of the action, however, with a piston system it really doesn't matter.
That being said, I prefer a midlength for handguard length and asthetics of barrel/handguard ratio.