First, the Tower of Piza experiment is apocryphal. It simply wouldn't work. Surface area and air resistance are related, and so he'd need to lug two objects of drastically different density but exactly the same shape up into the Tower and then drop them.

What he actually did was roll the balls down an incline. This website has a diagram, theoretical discussion, and the citation from Two New Sciences.

To your question: it's in De architectura in a more-and-less correct form. The text is dedicated to Augustus, which gives us some idea of the time of its composition. The important passage,

If quicksilver be placed in a vessel, and a stone of a hundred pounds weight be placed on it, it will swim at the top, and will, notwithstanding its weight, be incapable of pressing the liquid so as to break or separate it. If this be taken out, and only a single scruple of gold put in, that will not swim, but immediately descend to the bottom. This is a proof that the gravity of a body does not depend on its weight, but on its nature.

Quicksilver, liquid mercury, is really very heavy. But Vitruvius is correct, you could fill a deep well with quicksilver and a coin will sink in it. A sponge, by comparison, will float on it. Something will sink in a medium if its density is higher than that of the medium - this is called specific gravity.

Galileo's important contribution was that the nature of the objects was also immaterial, it only mattered that they had mass. And, tangentially, Einstein's contribution was that they didn't have to have mass.

But no, he wasn't the first to call Aristotle out on his incorrect theory.