It depends on what kind of hunting you're talking about. The hunting my buddies and I do is to get out a work our tails off to find, move up on and take the game, whether it's waterfowl, pheasants, deer or especially Elk.
We're out there walking from dawn to dark and after dark walking out.
We've all are vets and know that we can and often need to keep pushing ourselves and each other to get to the objective and accomplish our "mission" (get the game). We did it then and we do it now.
So, I think being a vet with experience in military can add to the success as a hunter. It's not the only way to be good at that and not all who've been in the military are even hunters obviously.