As I understand it, the atlatl enabled much more efficient and powerful throwing without much loss of accuracy. A brief search for figures says it can hit a grapefruit at 40m range

"For an experienced atlatl thrower, the mechanical advantage of the atlatl over throwing with the arm alone is about 6:1. Thus, if you can throw a dart 15 meters with your arm alone, you could throw it about 91 meters with the atlatl."