As far as I know, Galileo is basically facing Aristotelian physics, not exactly Aristotle. He goes so far as to accuse the Aristotelians of not having read Aristotle directly.
Galileo's superiority over his rivals lies in the synthesis of mathematics and controlled experimentation. The latter was alien to Aristotle himself, who limited himself to observations and filled them with his peculiar metaphysical beliefs. In this, Galileo was very superior and therefore his system, corrected and increased, ended up becoming modern science.