Three pages and yet, so far, no one has mentioned the one real advantage for hunting that used to be in all the books and articles. The SOUND.
Perhaps it's a sign of the modern era, and the general focus on firepower & military style arms over everything else, I don't know, but it seems to be.
Yes, a semi is usually faster to shoot follow up shots. Carefully aimed shots slows it down a bit, but its generally still faster than a manual repeater, in equivalent calibers.
One reason, perhaps the main one is that the semi is a heavier rifle, and one recovers from recoil faster because of that. There's no free lunch, however.
There are two basic types of semis used for sport hunting, those guns patterned after military arms (or arms that were meant to resemble military arms) and those designed from the beginning as sporting rifles.
The military style guns run heaviest, and there is little that can be done to lighten them, unlike the earlier generations "military guns" (bolt actions), which created an entire industry sporterizing them. If you WANT to lug around a 8-10lb semi when you could be carrying a 6-8lbs manual repeater, by all means, go ahead.
The sound of the semi is what old time gun writers thought of as the primary advantage. Specifically the sound of the action, being "swallowed up" in the sound of the shot.
The "boom" of the shot seldom spooks game (what's that?? Thunder???
). The metallic sound of the action being worked (a kind of sound not found in nature) often does spook game. (what's that?? I don't know, but lets get OUT of here!
)
So, the sound of the action blending into the sound of the shot was thought to be somewhat of an advantage, something the game wouldn't automatically recognize as an unnatural sound, and one more important for hunting than the magazine capacity or the difference of a second or so faster aimed followup shot.
A 9lb semi is a joy to shoot, and a beast to carry. Since I carry a LOT more than I get to shoot, lighter and slower rifles appeal to me more for hunting game.