I know that some times cattle get fed grain for a few weeks before being killed. So, I'd have to guess that if for some reason a deer were eating grain, and switched due to the season or hunting pressure to briars and such, there may be a difference.

If you're concerned about the quality of the meat you should pay attention to a few key details.
- Kill them with good clean hits.
- Clean them up quickly.
- Age the meat properly.
- Don't use venison as a substitute meat in other recipes. Get good recipes that call for venison only.
- Do not over cook venison, and serve it on a plate that has been preheated.
- Try to make only as much as you plan to eat in that sitting.
- Buy a good book on aging/butchering venison so you can read more than I'm willing to type.

Meat tastes “gamey” for a few reasons.
-under a large amount of stress before being killed, like from a poorly placed shot and a long period of time before dying, or running them.
-Sick animal.
-Animal not properly cared for after the shot/kill.
-Meat not aged properly.
-Not a good selection of meat for a given recipe.
Over cooked.
Good luck,
KP