The main difference between Rooney and Kagawa's off-the-ball defensive movement is that the former runs after the ball, whereas the latter runs after the play. In the AM position, having the grit and roughness to come at players is a luxury skill, not really needed. It's way more important to always be there for the CM to support them.
Kagawa's coach back in Japan stated that this is what makes Kagawa special. It's not just that he has intelligence and brilliant technique. It's his constant moving around that makes him a truly great player.
It's easier to notice Rooney's defensive off-the-ball movements because he's chasing the ball more than anything. He's also way more aggressive. It's all very noticeable to the spectator. It's the same reason for why Carrick was underrated for so long. People didn't appreaciate all his movement in the other areas of the pitch, because it's hard to focus on what's happening in the areas where the ball isn't located.
All in all: playing with Kagawa in the no.10 role is like playing with an extra CM who's allowed to attack. Playing with Rooney is like playing with a mobile striker who's allowed to drop deeper. It makes all the difference in the world, and frankly, I'm surprised at how many people there are who can't see this. Rooney and Kagawa is essentially the difference between 4-2-3-1 and 4-4-2. None of the formations are better than the other, but the latter requires a much better midfield than we currently have. Which is why we should turn to the former, and let Rooney and RVP fight for the striker position, with Kagawa occasionally playing as winger.