Joe Mantegna popping rounds though a Girandoni 18th Century replica (the second gun). He's not even trying to rapid fire it: he could go much faster. More at: Air Rifles
Before you laugh at air rifles (BB guns), the 1790 Girandoni that Thomas Jefferson owned could fire 22 shots of .46 caliber lead balls (at 800fps), reload the tube with 22 more shots, and do it again. Each shot could take down a bear or elk (easily kill a human). It was used by the Austrian Army for a couple of generations, but they were expensive to make, and American invented cartridges obsoleted everything else (cartridges are powder, brass, bullets, and primer in one).
The Girandoni was used on the Lewis and Clark expedition to demonstrate to local Indian tribes the kind of magical firepower they had and that is why no Indian tribe attacked them. (They were terrified of the "Fires Forever" gun).
Modern big bore air rifles go up to .50 (or .80) caliber and can be fully automatic (>10 rounds per second), and the lethality should not be mocked. Though because they are much quieter (can be silenced more) and still have limited rounds, they would work "better" for the sniper kind of attacks -- the problem is that kind of mass murders are often deadlier, and last longer, and are harder to deal with.