His QB's may not be stellar but they win him championships and are more capable of winning games if need be. Big difference is he shows confidence in his play calling. Plus a better job of coaching them up.
He just needs to not hesitate on the long passes. He can't wait to pull the trigger. The receivers could also do a better job of playing the ball despite the passes being short.
The difference though is that when the game is put on their shoulders and they are asked to go win the game for them they usually do.
I think a lot of it has to do with coaching them up better than LSU. But a big factor is Saban is also a run first coach but he isn't afraid to throw. He throws to keep the D honest, even though he is a conservative coach as a whole. Miles is uber conservative in his play calling. Miles handcuffs his QB. That plays into the psyche of the QB and the receivers. So they play tight when called upon.
Check this out - good analysis and highlights of Harris' incomplete passes last night: http://www.scout.com/college/lsu/story/1595367-another-look-harris-incompletion-streak Can he be better? Sure. Take a look at this story. This is not all on him.