What exactly do you mean by "play better"? Because it feels exactly the same on defence when I'm using a guy with 66 defensive awareness or when I use a guy with 33 defensive awareness.
It's generally easier to make steals or blocks with players who also have a higher Defensive Awareness - working together with the Stealing and Blocking rating of course. It's usually been a rating for the CPU though, determining how tough a player is on defense when the CPU is controlling them.
I think it's just of the same effect as higher steal and block ratings on defensive play,the player with higher defensive awareness ratings will react more quickly to opponents' offensive play,offense the same.
Is this what controls where or not the CPU runs a fast break or not?
Sometimes a player who's ahead of everyone else will just turn around and stop to catch a pass (and it's not a badly thrown one, he doesn't need to jump), letting everyone else catch up to him. Rarely, he'll catch it in-stride while automatically heading to the basket.
Does defensive awareness affect how quick someone comes in from the helpside? Sometimes players just stand on the opposite side of the ball and watch the guys on the other team dunk.
It does affect things like that, yes. Players with higher awareness ratings usually play a lot more intelligently and can better utilise their offensive and/or defensive abilities.