The rifle being used by more elite sniper units today than any other is actually made by a British firm called AI, for Accuracy International. Wired has a great piece about them. Go read it. In 2009, Craig Harrison was using an AI rifle (in .338) when he made two consecutive kill shots in Helmand Province at 2,475 meters.
That’s a mile and a half. Twice. In a row. My guess is that you can’t do that with a deer rifle.