I ate hobby farmed raised beef, pork, chicken, ducks, geese and turkeys. The veterinarian came around sometimes to check on stuff for us but I near never saw him inject or prescribe any medications. It took a bit of getting used to store bought eggs and chickens and the meat was not as tasty I think. All of the animals had fresh cut green grass to eat near everyday in the green months and green pasture was provided for the cow, heifer and steer, the pigs ate what we couldn't and the chickens the same. Now that I'm adjusted to store bought I just spice the heck out of my meat. Lots of basil for pork, beef and birds with rosemary for pork roasts, salt, pepper etc and even cumin.I hate chicken unless it's Southern Fried (and even then I only like the dark meat). In China they have been told that the dark meat is healthier, that the oiliness is essential to a human's well being. The truth is that there is very little difference nutritionally between the 2.
As to venison, it makes great chili, spaghettis, sausage, burgers, etc. I usually mix a bit of pork or bacon in with mine. I'd rather eat any wild meat than any meat grown for the supermarket.
But, on average, out of all the wild animals, the deer have eaten more GMO stuff than any other. It's a giant experiment by big agriculture.
Maybe not any better for us than super market non-organic chicken.