I think it's fair to say both players will perform for their clubs respectively. Sanchez, as he's proven in the past is more likely to be a bigger hit at United. That much is obvious.
However as an Arsenal fan, i'm giddy. We've had months of dark clouds circling over the club, apart from Wenger the Sunshine is starting to peep through the holes. Ask any Arsenal or neutral fan - Mkhitaryan's home debut for Arsenal was one of the best I've ever seen (at Arsenal). He was 10/10. Faultless, attack and in defence. A you're aware he is capable of such performances, if he can get some consistency or not remains to be seen - another point as he hasn't proven it like Sanchez has.
But the key fundamental differences of the players is that Sanchez is more of an individualist, if the team is playing crap he can produce that moment. Mkhitaryan seems to excel when the team is functioning properly. Again I think Arsenal is more suited to his play style as Rooney correctly pointed out.