Hey there. The only motivators you have for giving AA are Def stacking, Stun chance (on super) and maybe debuffing. Passive skills that involve things like decreasing atk or def for whatever amount for however many turns only trigger for the first attack, unlike super attack effects which can trigger as many times as a super attack is launched in a turn, so passive skills don't incentivise giving AA.
Putine has a medium chance to stun for her super attack, and that's it other than dealing damage. If you feel like you are so desperate for any chance at a stun on the teams you'd put her on that you'll take an initial 30% chance to stun, followed by a chance to launch another super attack which will have a 30% chance of stunning, then go AA, again, if you're desperate.
Otherwise, go crit. Apply this logic to any other unit and you should be able to make your own call. It would be more reasonable to go AA if it was a high chance to stun, but at medium I'd say go for Crit anyway and get a more consistent stunner to maybe give AA to.