I've found that what the deer eats has very little to do with the flavor. The deer I shoot in the woods where I now live are just as good as the one's I used to shoot in the corn fields. I've never noticed a difference between those that perished quickley vs those that were tracked for a day.
What is very evident is the way they are handled after being shot. Getting them completely gutted, hanging and thoroughly rinsed, rerinsed, and rinsed agian, asap is criticaly important, the quicker the better. All is not lost in the first 24 hours, but not rinsing and waiting for days before butchering will add to the gameyness every time. Deboning rather than cutting bones in the butchering process also plays a big role in the flavor of your meat.
I now pretty much only hunt deer in the morning so when I do get one it's in the freezer that day. (Warm meat is easier to cut up because your hands don't get cold and you don't have to trim around all the dried out stuff - or throw it away.)
.44 Special: For those who get it, no explanation is necessary. For those who don't, no explanation is possible.