I took two deer legally in Texas within seconds of each other because I had a semiautomatic. The .308 hit the "off switch" of the first deer and it collapsed without a single twitch. Because of that, the second buck standing only a few feet away from the first one was not startled except to look up because he heard a gunshot. There was not a single sound after that (i.e. loading another round), so all I had to do was adjust my aim and take the second deer. I have no doubt that working the action of a repeater would have startled that deer.
I hunt with a lever-action (deer, .308) or bolt-action (elk, .30-06) in Nevada, where I can only take one animal anyway. But for the spot that I have access to in Texas, when the deer do come around, there's often more than one of them, and you get up to five tags for whitetail, depending on sex and county. I'll always use a semi-automatic unless I'm down to my last tag.