Obviously. I believe his NFL stint made him reevaluate himself, and he's made the necessary changes in the way he does things. The result. Alabama's 3 NC's since '09, and his ability to keep Bama in the NC hunt almost every year since.
So theoretically If he came back to LSU, LSU would dominate college football? I'm not so sure about that.
I honestly believe had there been an opening, and Saban had come back to LSU that LSU would be the one riding this streak of multiple NC's and winning success. But then again, would LSU had given Saban everything that he enjoys at Bama? Bama was pretty desperate to get back to the top of CFB.
The better coach part is all Saban. But I'm sure what Bama has given him in terms of money to do things makes it a little easier.
I'm talking strictly abut Saban the coach. One easy and glaring example of his evolvement is passes to the RB and TE against his D. Teams could throw the ball at will to the RB and TE against his LSU defense no matter how good they were year after year. He has adjusted and improved.