That's not a slingshot, it's a catapult (except in America, where they don't talk proper). A slingshot has no elastic components, and relies for it's power on extending the effective length of the thrower's arm.
[YOUTUBE]https://www.youtube.com/watch?v=vDjL5uOs-8A[/YOUTUBE]
Both can be very powerful; The problem with ancient weapons is not that they lack power compared with modern firearms; but that they require far more skill and training to be effective.
Guns are 'better' because any moron can learn to be effective with one with very little training - both physical training to build muscle strength, and training for accuracy, are far less important with guns than with bows, catapults or slings.