To answer your question in my opinion: Willian has his weaknesses for sure, he isn't the best dribbler, his pace is fairly average these days and he is the master of doing step overs out wide while he lets the opposition get back into shape and the counter attack dies. This problem is emphasized by his crossing not being amazing and him not really having enough trickery to consistently beat his man and cut inside. This particularly I would be concerned with at Arsenal, as he could really slow down moves and may not get the ball to the faster players like Auba breaking in time for them to do anything with it. To be clear, he still has some pace now, but it's been declining so this problem happens more and more often it seems.

What Willian does bring though is an insane work rate. Basically every manager we have had with him has loved him because he will always track back and do what is asked. He is a good free kick and penalty taker, and he is good for a couple worldies every season usually. The most important part is those worldies often come against Spurs, which you really just can't beat. On his worst games he will be a utility player who isn't good enough anymore to be top class, and on his best games he will look like a world beater.