Of course. Store bought beef comes from large slaughterhouses. These companies only care about profit, that means they want things to be cheap, fast, and profitable. They pump the cows full of growth hormones and antibiotics to speed up the time it takes before slaughter. Many are diseased and stressed, which makes for unhealthy meat. Not to mention incredibly cruel and unethical.
Obviously grass-fed deer living free is much more healthy. If the person shoots the deer in a way that makes death instantaneous, or very quick, adrenaline won’t pump through the meat (I’ve heard that it gives it a gamey taste).
By the way, stay away from corn-fed beef. I am a vegetarian, so I’m not very knowledgeable in this area, and I forget why this is important. Watch the movie Food Inc if you want to learn more about this sort of thing, it explains what’s so bad about corn.