Back in 1958 my father went on an elk trip to central Idaho. He met a forest service ranger, who mentioned that elk and deer often freeze at the sound of a rifle shot, but run when they hear the metallic sound of a bolt action. He showed Dad his Remington 740 Woodsmaster in 30-06. He claimed to make easy follow-up shots on deer and elk without spooking them.
Fast forward to 1988, my dad retired but arthritis set into his hands and fingers. He tried both bolt and lever action rifles but couldn't operate either. So we bought him a 7400 Deluxe. On hunting trips for the next 17 years I loaded the magazine for him and inserted it in the receiver with the bolt locked open. He could close the bolt and flick the safety on and off as he wished. He got his deer and elk with it. Once in 2002 I borrowed it, and I got a deer. I would expect that you can be just as successful with an autoloader, if that's the rifle you want. It's a personal choice.