What is the difference between modern and ancient cosmology?
Depth, detail and models of the universe.
Ancient (I'm going to use Astronomy because Cosmology is a Russian term, not that I have anything against Russia but that I'm not sure if it is accurate) astronomy mainly focused on the movement of celestial objects based on the position of the Earth.
This was known as the geocentric model, where the Earth is the centre of the universe. This has some problems because it could not explain the problematic and irregular motion of a lot of celestial objects.
We now use an expanded version of the heliocentric model, where there is no centre of the universe, but where we are rotating around our sun.