Which model is more accurate, the Ptolemaic or the Tychonic?

If by 'better' you mean more accurate, the vote goes to the Tychonic. Ptolemy put Mercury and Venus in the wrong place, having them orbit the earth when they actually orbit the sun. But he was clever: he left six variables in his model so it could be adjusted once we knew where Mercury and Venus belonged, which is good foresight for a man of the first or second century. He also invented the equant, one of the most ingenious devices of the first millennium, an added radius connected to the planet that could be adjusted to compensate for what we later found with Kepler, that the orbits are elliptical rather than perfectly circular. The equant did this so well that it was basically equal to Kepler's elliptical orbits. In fact Giovanni Riccioli took Kepler's elliptical orbits and put them into the Tychonic model, because the original Tychonic model, like Copernicus's, used perfect circles copied from the Greeks. That is one reason Copernicus's model never worked; he needed even more epicycles than Ptolemy, ending with forty-eight to Ptolemy's forty, so the claim that Copernicus was simpler is a myth. With Riccioli's elliptical orbits, there was no real difference between the geocentric and heliocentric models. Then Newton shut the door in favor of heliocentrism, but only by confining the system to the sun and planets and excluding the rest of the universe. Two hundred years later Ernst Mach pointed out that you have no right to do that with all those stars out there, and the question reopened.