I personally didn't really feel much of a difference. I did a little better when I went back to normal Crucible, but I only did better there because all of the HC players were in the Iron Banner. I saw the whole spectrum of levels and killed as well as got killed by all of them.
There are probably videos and info being uploaded/written right now that are breaking it down to prove whats really going on. I have already seen a video of a player using 2 different characters each different levels using the same gun and the damage stats didnt change. Nor did it appear that it took any less or more shots to kill with it.