IMHO, AJ's a shooting guard in a point guard's body. He's a streaky shooter, but when he's on, he can score 10 pts in a quarter for you. He uses screens very well.
As a point guard, he lacks the necessary instincts offensively. Defensively, he's at least average, which ain't bad for a guy his size.
On the Bulls, he had his best moments late in games when he was inserted late to add an offensive spark. He's definitely isn't afraid to take big shots at crunch time and he isn't discouraged when he misses. I imagine if he shows this characteristic on the Lakers, Shaq, Kobe and Phil will get in line to punch AJ's lights out.
His best use is as a Steve Kerr-type shooter. When last seen here, he lacked Kerr's consistency, but is certainly less of a defensive liability than Kerr.
AJ is going to fit in perfectly with the Lakers. There is really only one thing AJ does well, that is shoot an open trey. He'll get plenty of open looks in the triangle w/ Shaq Daddy in the middle and a slashing Kobe.
I disagree with some that say AJ plays defense okay. I haven't seen it, and I've watched almost every Bulls game the past 2 seasons. AJ is basically a spot up shooter. He can't create for himself or run the point. He'll be a nice fill in if Fischer or Horry get cold from the outside.