With my computer broken, I have been trying to play the 360 version and I noticed a significant difference in the response time from my control input. I am really sensitive to this kind of thing, especially after playing the pc version and not experiencing any lag.
In a game where quick reactions and precise shot release timing can make the difference, any lag makes the game unplayable and takes away from the enjoyment as the game takes longer to respond than it should. I'm not talking about the over exaggerated lengthy animations, which add further frustration.
I thought it had to do with my tv, but I played the pc version on the same tv and have noticed a difference. Other xbox games don't seem to have this problem.
I've tried many things like changing the xbox display resolution to using a wired controller and installing the game to the hard drive and it made no difference.
Try this experiment if you have the 360 version. Start a game, then pause it. Go up and down the menu to get a feel for the response. Now press the xbox button on your controller and go up and down the menu. Notice how the xbox menu is much more responsive than the in-game menu is?