The record is quite damning; Arsenal have failed to win a Premier League game without Mikel Arteta, losing 3 and drawing 2 since his arrival. It makes him one of Arsenal's most important players, as the midfield looks somewhat disorganized without him. In his absence, Aaron Ramsey has been given a deeper role, but he hasn't flourished. He quite clearly prefers playing higher up the field, as evidenced by his switching with Tomas Rosicky. With Ramsey struggling, though, when he has played deeper, he's been unable to exert his influence on Arsenal's tempo. That was particularly evident against Chelsea, when Arsenal looked somewhat broken. When Rosicky got on the ball, he was somewhat able to dictate Arsenal's tempo, but it didn't happen enough before he came off with the effects of his flu. After losing Cesc Fabregas, Mikel Arteta took on the role of dictating Arsenal's tempo, giving Ramsey or Rosicky the freedom to create. Rosicky is the obvious candidate to take on that role in the absence of Mikel Arteta, as he is the Arsenal midfielder best able to control the tempo.
The problem, though, is that Rosicky hasn't been getting the ball as much as he was with Arteta in the side. The disorganization that has plagued Arsenal's midfield has meant that there isn't the link man between defence and attacking midfield, unless Arsene Wenger drops Rosicky back. As such, without the ball, Rosicky has been less influential, affecting games in moments rather than throughout the 90 minutes. As such, Arsenal's creativity has suffered, and they've only scored twice since Arteta went out injured. It's not that Arteta is the playmaker, it's that he's the player who links defence with attack. It's a problem that Rosicky is aware of; in the recent Arsenal magazine, he made the point that he can play deeper: " As I have said many times before, I can play this role too. I can drop a bit deeper too but let's see what the boss wants."
With Rosicky deeper, Arsenal might lose creativity further up the pitch, but Aaron Ramsey has improved, and they still have the threat of an Alex Song throughball. Rosicky's renaissance wasn't based on the ability to play defence-splitting passes; while he did do that, his better form was more connected with directness and pace, and adding urgency in Arsenal's game that had been lacking. He can still do this from deeper areas, much like Jack Wilshere did last season. In one of Rosicky's best games, against Sunderland at home, he made a fantastic run from deep, gathering pace as he went on. From a deeper area, Rosicky has more space to get away from players and make driving runs, a feature of Arsenal's play that's been missing this season.
One can see, though, why Ramsey's been playing in Arteta's role. The Welshman is much more of a knitter of play than a playmaker, with Rosicky filling more of the latter role. With the two, there is some overlap; Rosicky rarely plays the final ball, but remains direct and forward thinking, while Ramsey likes retaining possession but can play the final ball. Because of this, it is perhaps better if Ramsey plays forward and Rosicky deeper; Ramsey can retain possession while Rosicky can create from deep and impose his influence on Arsenal's tempo. There's also the point of having an experienced, calm head in the midfield, who has a knowledge of when to slow play down and when to speed it up.
Ramsey and Rosicky played together earlier in the season, before the purchase of Arteta. Against Udinese in the Champions League, Rosicky played deeper than Ramsey, and Arsenal were fairly solid in open play in those two games with that midfield partnership; Rosicky got back and made tackles and also knew the right time to press, and, positionally is far better than Aaron Ramsey. He also got more time and space to create. Ultimately, Arsenal's best use of their available midfielders will be to use Rosicky deeper; he can dictate Arsenal's tempo and create from deep, while Ramsey can knit play further up the field and try to create for Robin van Persie, as well as get into decent scoring positions.