I'm quite familiar with both weapons. The way I see it, a sling vs. a bow is sort of like a dagger vs. a spear: they both exist for a reason, but except for specific situations, you'd probably be better off with the spear.

The show The Deadliest Warrior is absolutely awesome if you're into this stuff. They've had a few appearances of the sling, notably with the Gladiator. Generally speaking, the sling didn't measure up well.

• Arrows win hands-down for accuracy. Throughout many appearances, archers could easily hit a stationary target in the eye, and consistently hit moving targets fatally (major artery, etc). Slings were so-so.

• Arrows win hands-down on range. The sling isn't nearly as accurate at range. Also, air resistance was slowing them down enough to make them non-lethal.

• Slings were largely non-lethal. Unless you got a head shot, it was nearly impossible to land a fatal blow with a sling, even using lead shot. Even the experts had trouble pushing over 100mph, and anything less than that simply isn't a kill shot.

• The sling would definitely win in high wind, although they didn't test it on the show. However, in the article, they definitely overstate the effect of rain; unless it's really windy, arrows hardly fly differently at all, I find it quite easy to shoot in the rain.

From the article:

"Arrows, unless barbed and deep in the victim, are easier to extract"

Many/most were, and making barbed isn't much more time-consuming than making a traditional arrow head. In The Deadliest Warrior, arrows very consistently pierced about 1.5 inches into flesh.

• Armor - even padded leather is sufficient to neutralize stone and take away crippling effects of shot.

Julius Caesar writes about clay shot being heated before slinging, so that it might set light to thatch.

Nice try, Julius.

There was also a belief, presumably false, that sling bullets got white hot as they flew through the air

As a tl;dr for the episode, against an opponent with leather armor, the sling hardly more effective than throwing rocks.

Lead melts at a much, much lower temperature than that.

When iron plate-armoured Spaniards went into South America against the Aztecs, ...the sling stones would damage the Spaniards by sheer smashing force.

I call shenanigans.

Thanks for the interesting read though, sorry to pick it apart. The sling definitely wins for versatility, ease of construction (really just minutes, and out of anything), but for power, accuracy, and potency, the arrow wins, hands down.