I prefer to hang and age my deer when possible. It helps a lot if you do everything right. Slaughterhouses don't hang and age beef because they want to waste time or have lower quality. But it isn't often that you get the ideal conditions to do so.
Good tasting venison starts before you pull the trigger. I try to hunt mostly in places where the deer live close enough to agriculture to have a good diet. Deer that are browsing on quality feed like corn, clover, alfalfa, apples, white oak acorns, etc. are naturally going to have better quality meat than deep woods mountain deer that are browsing on lower quality wild grasses, various leaves, etc. If I have time after gutting, I usually slice the rumen open to see what it has been eating, and learned they'll travel a couple miles to get standing corn. Deer that are expending more calories climbing steep terrain won't have the same percentage of body fat as crop fed deer that are able to consume adequate quality food with minimal effort, and are spending more time resting and chewing their cuds. The same rules apply as for raising good quality beef cattle.
I strongly believe that it makes a big difference how you kill the animal. A farmer I know who raised very high quality beef that he sold to expensive N.Y.C. restaurants told me that he kept his cattle mostly confined so they weren't grazing and walking a lot to build up muscle. He fed them the highest quality feed, and said that when he slaughtered them, he did his best to keep them very calm, and gave them beer to drink so they would be very relaxed when they were killed. He said if they were alarmed or agitated, they would produce more adrenalin, and that would affect the taste and tenderness of the meat. So it goes with deer, elk, etc. If you gut shoot your deer, and it is suffering and alarmed while you are tracking it, that is going to adversely affect the meat. I like a high heart or aorta shot, because the lower chambers usually keep pumping. The deer's blood pressure drops to about zero immediately, and much of the blood is pumped out into the chest cavity. Death is immediate, or within seconds.
I don't field dress my deer. I always take the extra time to hog dress them, because opening the chest cavity and removing the heart, lungs, esophagus, trachea, etc. allows the carcass to cool much faster. You should be very careful to do a clean neat job. Any dirt, debris, stomach contents, or urine from a sloppy dressing job is going to introduce bacteria, which will lead to quick spoilage during any hanging and aging. Avoid getting any debris in the body cavity during dragging. Then you need those rare ideal hanging conditions. Since most of us don't have access to a large cooler like slaughterhouses use to age meat, the carcass should be hung in an unheated garage or shed, out of sunlight and wind. If temps are on the warmer side, getting the hide off quickly helps the meat cool, to reduce bacteria growth and spoilage. Then you need several days where the meat remains at refrigerator temperatures ( between 32° F and 36° F; never higher than 40° F) during the day, and doesn't get so cold at night that the meat freezes. It isn't often that you get those perfect temperature conditions for more than two or three days. I've only had those near perfect conditions last more than four or five days a few times in my entire hunting life, and was able to hang my deer eight days once. But even a day or two to get the blood out of the carcass is better than nothing, because rigor mortis may last 24 hours or more. I made a spreader to hang the carcass neck down, by the back legs, which helps keep the body cavity open for cooling, and allows blood to drain out of the better hindquarter and backstrap cuts. Excess blood in the meat is fine if you like steaks, chops, and roasts that taste like liver. I don't.
