There's a certain amount of personal preference involved. I used to work for a butcher. and we sold primarily box beef (not aged) through the counter. We got a contract to handle sides and quarters from a local farmer, and the meat was aged for a while (over a week, can't remember exactly). Some people loved it, others complained that it wasn't like what they were used to.
Deer I hang for a day or so, but that's about it. Whatever you do, skin it immediately to allow it to cool faster. I also have a trustworthy processor with a walk in that I use if it's too hot, and he lets them hang a little longer.