If you hang your game until it is in full rigor (a couple of hours) you have 90% of the benefit you will get from any amount of aging. Most of the time, it will be in full rigor by the time you get it out of the woods, unless you can drive right up to it. Best results are if you can let it set up with the muscles at full extension. Aging can add some quality, IF you have a fully controlled environment (38 degrees, near 100% humidity, absolutely sanitary surfaces, clean air), no bloodshot meat, and no contamination. Aging is, after all, a controlled decomposition process. If you don't have control, all that's left is decomposition. Hanging an animal in the garage for a week is not aging, it's bacteria farming. I've hung meat before, but these days the only time I will hang an animal is if I shot it close enough to home that it has not gone into rigor yet when I get it home. If that's the case, I will hang a deer head down for a few hours. Otherwise, it goes right into butchering.
Dry aging is a different process, that is done with individual cuts or primals in the refrigerator. It can be done, and if you don't mind losing 5-10% of your meat to crusting it can improve flavor and tenderness a bit. I may try it if I end up with a lot of deer and elk this fall. Usually I am really stingy with game meat and don't want to risk losing any.
The major players in game meat quality are cooling the carcass immediately, keeping it clean, getting rid of all fat, hair, and bone in contact with the meat immediately, and not overcooking it. And remember it is not beef or pork. It does not respond well to being cooked like beef or pork.