Which weapon can transfer more energy to a projectile: sling or slingshot? Which weapon can transfer the most energy to a projectile, a sling or slingshot? 
Each is totally powered by a person, one stores energy in elastic the other kinetically. Which can store and transfer the most energy to a projectile?
For a fair comparison, limits are completely human powered and supported. No slingshots anchored to the ground. No Trebuchets.
 A: Although there are physics involved, this is largely a physiology question. 
A slingshot can impart as much energy to a projectile as the user can transfer to the bands. If we assume bands that are strong enough to withstand more stretching than any human can manage, it will depend entirely on his pulling strength.
Similarly, a sling can impart as much energy to a projectile as the user can transfer to the sling. But unlike a slingshot which uses linear acceleration, a sling uses angular momentum since slings are generally "fired" by spinning the sling rapidly and then releasing it with a final motion of the arm adding additional energy.
If we assume the user can impart the same amount of muscular force to either weapon and is equally skilled in using both, then the sling wins because that final motion of the arm is imparting energy to a projectile that is already in motion and therefore already has stored energy, while a slingshot is imparting the same amount of energy to a stationary projectile. Some of the energy the slingshot user can muster will have to be used just to accelerate the projectile from a standstill to the same speed the sling started out with.
A: With my slingshot I can launch a 1/4" ball bearing maybe 60 yards.  With my sling I can launch a 1" ball bearing maybe 120 yards.  The science/engineering guys can give you a more precise answer, my experience says the sling imparts more energy by something like at least an order of magnitude.
