He came on in the second half against Netherlands today. Japan instantly looked so much better.
The two highlights for him were when he received the ball centrally about 20-25 yards out, dribbled past a defender, and fired a good shot on goal with his left foot. It took a great save from the goalkeeper to stop it. The other highlight was his perfectly timed defense-splitting pass. Kakitani was alone on goal, but missed his chance. Had that been Rooney or RVP, it would have been a sure goal.
Say what you want about Kagawa, but for Dortmund and Japan(which play totally different styles, mind you), Kagawa has been bossing the game against opponents like Argentina, Italy, Netherlands, Bayern, Schalke and many other fairly strong teams. What Japan and Dortmund have in common, is that there's a lot of off-the-ball movement. Even if Kagawa plays slightly more to the left for Japan(though not nearly enough to be called a winger), he still has several players making lung-busting runs around him.
At United, we seem to value defensive stability, which again leaves little room for all this movement. That's why I think Kagawa wont cut it on the wing. It's not that the PL is too physical that makes things hard for Kagawa. It's the fact that we play with too little movement. That's why I'm sure that he'd shine for Arsenal(for instance).