the correct answer is: it depends!! Depends on terrain, cover, game, rifle you have with you, load,optics, time of day, etc, etc, etc.
The last 5 deer I have taken with one exception, were all killed at distances less than 50 yards. The rifle I used was selected for heavy cover, short range work. the exception was a shot at about 250 yards, using a different rifle, because in the area I was hunting, there was a 50/50 chance that the shot might have to be taken across a pasture, not in the heavy cover I usually prefer. Good planning, and knowledge of the area paid off.
I realize that hunting in Florida swamps and palmetto thickets is different than hunting in the Rockies. In mountain areas, or the wide open plains, I am sure I would use a different rifle than the .44 Mag Marlin 1894S, or the short barrel Mannlicher-Schoenauer in 8mm Mauser. I have never been one to take a shot at long range, if I could get closer. Stalking is, to me, half the fun and challange of the hunt.