You obviously know the difference between a sling shot (rubber bands) and a sling (which is whirled and released). The most powerful wrist rockets are capable with accuracy and enough power with a ball bearing for instance, to kill with a head shot. However, the sling, with a boiled egg for instance (the projectile of choice in some areas and the original war-projectile in many areas) is capable of crushing the skull and capable of more range and equal accuracy.
I too prefer the firearm. However my argument here is partly that we forget the ease and power of the sling and that we can take stones and a sling anywhere!!!! When I go to the woods where there are dogs and cougars -- I don't even consider a sling or sling shot for defense and personally I would not even IF I were good enough. Make mine 9x18, .9mm, .45, .44 mag, .357 and most of all .223 and 12 gauge. But none of those will pass muster in an airport, a police search, or any other kind of check. A few pretty rocks some 550# cord and a piece of leather would not get me stopped anywhere, I'll bet.