Here are a couple passages from Cassius Dio's Roman History that mention the sling.

For since he [Ventidius] neither hindered them [the Parthians] crossing the river nor again attacked them near the crossing, they imputed weakness and reluctance of the Romans, and from this they rode up to their defensive wall although it was on high ground so as also to seize them. When a sally suddenly happened, [the Romans] drove them away without difficulty down hill, inasmuch as they are horsemen. Thereupon they defended themselves courageously (for most of them were kataphracts), but they were thrown into disorder by the unexpectedness and by one another, they were overcome by the heavy infantry and by the slingers most of all, for the greatest difficulty reaching them came from a distance by the powerful throws. (Roman History 49.20.1-2)

Coming together with the Parthians, Antony put them to flight: for his slingers were many and all of them threw further than the archers, and they maltreated the kataphracts severely; and yet he did not destroy a significant number: for the barbarians rode fast. (Roman History 49.26.2-3)

I think that these passages are interesting for a couple of reasons. First, they show that the effectiveness of the sling is not necessarily a function of the body count. The very Parthians who Anthony's slingers "severely maltreated" had earlier wiped out a large detachment of Romans. Even if the slingers did not kill many of the Parthians, they probably saved Anthony's army.

Second, they confirm that the sling's lethality depends on context. When Anthony faced the Parthians, they were mobile, and a fast-moving target will be harder to destroy than a stationary one. Moreover, even if the sling has longer range than the bow, rocks or glandes will be less effective at the edge of bowshot range than they would be up close. By contrast, when Ventidius' slingers faced the Parthians, they were massed together and disordered at the bottom of a hill and being assaulted by infantry (and perhaps also pinned against a river). If you're being attacked by slingers, it's hard to imagine a worse situation to be in.