@heme725I personally see a difference most of the time, controller players have this jittery movement, sometimes it feels/looks like they can turn only at 90 degrees 🙂
Mouse and keyboard, in my opinion, is much smoother and I guess that's the basis why AA exists on the controller.
Regarding the video - I will be honest here, this player's tracking and decision-making at times are not only average but below that.
Also, people usually play their best guns and clearly, the guy's loadout is not "poor" thus I assume he did pick to run Flatline and R99 rather than playing them because those were the only top guns available. Yet he still misses so much with Flatline = for me an indication of his abilities when AA is not there.
Finally, check two situations - when he tries to kill Pathfinder from point-blank range and when he shoots at Bangalore.
On Pathfinder his aim is all over the place to say the least even though the distance is close to 0 = dude clearly panicked and overshot aiming with his controller same as he did in most cases with Flatline in the distance.
Yet on Bangalore cursor keep going back to the target multiple times.
As for your rhetorical question about what is best where - from my experience at close range controller is superior as I personally play on very low sense (0.2 sense with 3900 dpi) and I am working on my close range fights as I usually overshoot target by ~0.5cm (measured on my 31.5" screen) while being in my opinion quite good in midrange fights.
Overall though I would rank input modes like this:
1. M&K with AA - xim and stuff 🙂
2. M&K without AA
3. Controller with AA
4. Controller without AA
And based on the above I see that frustration about cross-play an AA availability on controller comes from the fact that it is very annoying to have a fight like this - where you clearly dominate mid-range game (in video example where dude misses most of his shots with Flatline) and then suddenly such player is "in your face" and beams you. Basically flipping a switch and going from Silver/Gold to Diamond in a moment so to say. Be it Eva, Wingman or full clip of automatic weapons.