You're right, mathematically speaking the two systems are the same. As a matter of fact, the calculations that describe the attitude of a spacecraft flying not far from the Earth are usually expressed in a geocentrical reference frame. It's much simpler, yet produces the same result you would get using the heliocentric frame.
The real disadvantage of the geocentric system is that it is a barren model: it does not allow science to advance. It is able to explain the motion of planets with exceptional precision, but it does so by using a mathematical construction (the epicycles) that does not lead to a deeper understanding of the inner laws of nature. On the other side, the heliocentric model (when corrected with Kepler's idea of using ellipses instead of Copernicus' circles and epicycles) was a big step towards the bigger understanding of gravitation that was produced by Newton's law of gravitation.
The real disadvantage of the geocentric system is that it is a barren model: it does not allow science to advance. It is able to explain the motion of planets with exceptional precision, but it does so by using a mathematical construction (the epicycles) that does not lead to a deeper understanding of the inner laws of nature. On the other side, the heliocentric model (when corrected with Kepler's idea of using ellipses instead of Copernicus' circles and epicycles) was a big step towards the bigger understanding of gravitation that was produced by Newton's law of gravitation.