I have an opinion. No facts.
I would expect the AAs to be loaded with hard shot.
AAs would be 3/4 oz. Many of the 28 gauge hunting loads are 1oz.
If you are pass shooting mourning doves then your shell and choke selection probably make a difference. If you are shooting bobwhites over pointing dogs it probably doesn't make any practical difference which shell you shoot.
My favorite bobwhite load for my Parker 28 reproduction is the AA #8s, 3/4oz., ~1200 fps. The little repro is choked 40 thousandths and 40 thousandths.