Further to markjo's point:
In RET the stars moving slower than the sun is an illusion. In FET the stars really are moving slower than the sun.
The stars appear to move relative to the sun in the same way a tree in the middle distance appears to move relative to the hills behind it when you are driving along the highway, looking to the side. In FET, there is no real explanation of how the stars are supposed to move, or the sun for that matter.
In RET the retrograde motion of the planets is an illusion. In FET the planets really are retrograding.
This one's a bit harder to think of an analogy for, but it's a bit like driving on a busy freeway, where you are going faster than some cars, and slower than others, and some turn and come back on the other side of the divider (clumsy analogy, I know, but it's the best I could think of right now). Again, FET has no real explanation of how the planets retrograde.
All in all, the round earth (real world) explanation is much tidier, and demands no special magical behaviour of celestial bodies or light therefrom (although I realise some still think of gravity as 'magical').