Jack Wilshere may wear the #10 shirt, but that is more sentimental, with the #10 shirt given to a player that Arsene Wenger believed would be crucial to future Arsenal success following Robin van Persie's departure, rather than telling about Wilshere's position. At times last season, Wilshere played in the #10 role, and played well, but his performances were too inconsistent to pencil him in the role permanently, and signing Mesut Özil has made it extremely unlikely that Wilshere ever play the role on a permanent reason.
There is a reason for this: the positive traits of Wilshere's games are better suited to a deeper position.
Arsène says: "His best position is as a deep-lying midfielder, where he can be a distributor. He has a good burst and vision" #AskArsene— Arsenal FC (@Arsenal) November 12, 2013
From a deeper position, Wilshere can use his distributing skills, and he's perhaps the best midfield Arsenal have at linking play. He also becomes better at dribbling; perhaps he has more space, or, he can gather up a head of steam, but either way, his close control is seemingly better from a deeper position than when he plays wide.
It's also better than when he plays as #10. For a player to be good at #10, they have to be comfortable playing almost with their back to goal: a lot of their play can happen under pressure from defenders, and instead of playing with the defence ahead, they have to receive the ball with their back to goal or side-on, and then turn. This doesn't suit Wilshere's game: Wilshere prefers to receive the ball in deeper positions, with the game in front of him. Wilshere's best trait is his ability to drive the ball forward, by dribbling and playing one-twos, and with the game in front of him, he can drive into space. Wilshere is far more at moving into creating space with the ball, rather than creating space with movement, like Mesut Özil, and that's a major reason why he's better deeper than at #10. From a deeper position, he can survey the pitch, and either switch play, or drive into space further up the pitch before playing attacking areas into a position where they can either create or score.
Of course, the problem for Arsene Wenger and for Jack Wilshere is that Arsenal have another young central midfielder, who is obviously better in a deep central midfield position. That man is, of course, Aaron Ramsey, and deciding which of two is better has been a topic for debate since 2009: first it was Ramsey, then Wilshere, and then Ramsey, with form relating to injury perhaps making it impossible to truly compare the two. But with Ramsey now fully fit and over his broken leg, and with Wilshere getting sharper with every game, it is now more valid to compare the two.
Both are very good at covering ground--Ramsey has run the most distance out of all players in the Champions League, and as Wenger said, Ramsey wants the ball, hence, his defensive awareness has vastly improved over the past 12 months. He's also becoming a very good tackler: no player has won more tackles than Ramsey in the Premier League this season. Meanwhile, in the Twitter takeover, Wenger praised Wilshere's "tactical intelligence", and certainly, in recent games that the two have played together, there's been a better understanding when one goes forward, and when one stays.
The two attacking styles can help too: Ramsey likes to make late runs into the penalty box, and thus, can go later as the attack has developed, swapping off with Wilshere. Though Wilshere has added a goal-scoring streak as of late, his off the ball runs aren't as good as Ramsey's, who's late runs are truly exceptional. Both Ramsey and Wilshere are very adept at switching play, and while the Englishman has more subtlety in the final third, Ramsey has become better and better at playing little through balls, like the gorgeous assist for Serge Gnabry.
Arsene Wenger said that Aaron Ramsey always wants the ball, but the same could be said of Jack Wilshere too. Because of that, it's fair to say that both are box to box midfielders. The two should be able to form a double pivot in the near future; perhaps not now, as they need to gain a better defensive understanding, but in years to come, it could easily be Arsenal's first choice pivot. As for this season, the two will continue to develop without partnering each other, but if needed, the two can do a job--already, against Chelsea, they showed big signs of improvement in understanding.