The clash between the Ptolemaic system and the Copernican system was not only an astronomical issue. It was a key moment in which humanity had to face the terrible truth that we are immaterial to the universe. We are not at the center of the universe. Yet, such a loss (that Freud's labelled as the first great outrage upon human narcissism) came with a reward: Nature is much simpler once it is not longer requested to bend to please human vanity.
The Copernican system revealed a much simpler structure and was therefore to be preferred. Although it was not perfect, it allowed future generations of scholars to unwrap the principle of dynamics and the law of gravity. Sometimes, the strength of an insight lies not only in its precision but in its capacity to peer further in the structure of reality.
Formally and mathematically, the Ptolemaic system was equivalent to the Copernican system. Both systems were able to describe the movements and the trajectories of planets -- at least at the level of accuracy available in the XVI-XVII Century. However, the Copernica system was superior because it revealed the anti-humanistic manifold of physics.