If both are healthy, Tinsley should start. Unfortunately, that never happens. Tinsley makes the offense run so much better. He penetrate and dish, he is much better at feeding the post and finding open guys in general, and he's a superior passer. His handle also gives him a significant advantage; AJ often struggles with getting the ball up court in a timely manner.
Defensively, I feel that AJ is better. He doesn't play the passing lanes at much, but he's a better man to man defender. He also does a better job against bigger points.