I thought about mixing them, and you are right I could more easily set up a crossfire of both types;
AA and AT. But I'm finding that keeping your
AAs activation till last maintains your 'reaction fire' threat till the end of the turn. If you activate your
AA during the turn, your opponent will wait for it to shoot and then move his aircraft freely afterwards.
So having it all in one battle-group allows me to activate all other battle-groups first and then, if there's nothing else for the
AA to shoot at, and they haven't reaction fired at enemy, I can target infantry in a building with it.