What did galileo discover in his legendary experiment on the leaning tower of pisa?

Galileo reportedly dropped two balls of different mass from the Leaning Tower of Piza to prove that the time it took each to hit the ground was not dependent on the mass. Assuming two objects have a similar amount of drag during free fall, it will not matter whether one object is substantially more massive than the other object, they will fall at the same rate because gravity pulls on all objects at the same rate given that the objects are at similar distances from the object (Earth in this case) attracting them.