Whose system of the universe was most accurate?

One that hasn't been discovered yet.

The way science works is by observing the world around us, and trying to figure out how it works. We make hypotheses - guesses, really - about how things behave, and try to make predictions based on those guesses. We then do experiments that will test the hypothesis, and observe the actual results. We then share the experiment, and the results. We call this the "scientific method", and it ALWAYS works - as long as everybody is honest.

Because of this, scientific theories are constantly evolving. Scientists make new theories to explain new facts, and then we try to figure out an experiment to test this idea. We're never completely right, but we learn something new every time.

Ancient people had no special instruments; they used their eyes and ears to see what was happening, and they made explanations - at the beginning, often wrong ones! - about how things worked. For example, we're standing on the Earth, and we're not moving; isn't that obvious? We can't FEEL any movement! So when the Sun and Moon and stars rise in the east and set in the west, clearly those objects were going around the Earth. It wasn't until Aristarchus of Samos that they figured out that the Earth was going around the Sun, but Aristotle argued the opposite, and his views prevailed for almost 1600 years.

It was left to Nicolai Copernicus to calculate that the Earth - and all the other planets - were going around the Sun before that idea really took hold. Galileo's observations of the moons of Jupiter were the major argument; if Jupiter's moons were going around Jupiter, then not everything was going around the Earth!

Our modern ideas of the cosmos are still in flux; is there such a thing as "dark matter"? We don't know. Every new fact has to be interpreted in the face of every fact before it, and this process is nowhere near complete.