Venison definitely tastes better rare to med. Not overcooked.
The flavor is similar to a blend of lean beef and trimmed lamb.
A fast quick kill shot will result in better tasting meat than if it is chased and accumulates lactic acid in the muscles.
Quick chilling is important for preservation as well, or else the meat will spoil and taste "gamey."
So how the venison tastes depends on (1) what the deer are eating, (2) how quickly you kill it, (3) how quickly you chill it, (4) how long you age it, (5) how properly you prepare it.
It varies from unique and sweet to tough and gamey.