"But the bow was still powerful and deadly"

that was my only real point. i thought of the example of ,say, the Assyrians who almost always deployed slingers in tandem with archers. the supposition being that with the slingers in the front ranks shooting a flatter trajectory you'd have the archers volleying high over the heads of the slingers into the enemy ranks.

as far as wounds, yes, i'm betting that a sling bullet would have a better chance of inflicting an 'immediately' disabling wound on an armoured enemy. an arrow wound is easily staunched if it does hit a non vital area. a later period parallel i thought of was the fact that the prevalence of plate armour in the 15th c. brought the mace (an impact/concussive weapon) back into favor. not to punch through the armor, but rather to turn you to 'soup in a can'.