Adrenalin has a bad effect on meat given enough time so yes a calm/quick death without too much stress gives better meat quality.
It is safer to do a heart/lung shot though, too many variables that can go wrong with a head shot, it can result in a slow and painful death which any responsible hunter will avoid at all cost.
If I can't make a clean, safe, good shot, I'll rather not take the shot.
I think I know what most of us would choose if you get to choose between a life in the wild with the possibility of a sudden end or a life in the factory farms where the slaughterhouse is a certain last stop.