Tycho Brahe proposed a world view in which the Sun revolves around the Earth (i.e., geocentric), but all other planets revolve around the Sun (i.e., heliocentric). His world view lay somewhere between that of Ptolemy (all planets geocentric) and that of Copernicus (all planets heliocentric).
The model of Copernicus was immediately more popular than that of Tycho, and it has remained like that ever since. However, in principle, Tycho's model explains the movement of the planets equally well as the model of Copernicus does, so that provides no argument to prefer one of the models over the other one. None of the models (of Tycho, Copernicus, or even Ptolemy) as they were applied in the 17th century gave much more accurate predictions for the positions of planets than the other models, so that did not help to select the best one, either.
The choice for a particular model was therefore based on other arguments, such as opinions about "elegance" or "common sense", or about how well each model seemed to fit with particular interpretations of passages from the Bible, but people did not all hold the same opinions about these things, so both models had some fans.
Copernicus published his model in 1543. Tycho published his model over 40 years later, in 1588. In 1627, Kepler published the "Rudolfinian Tables" that were based on his new model of the Solar System with planets in elliptical orbits around the Sun, and these tables provided more accurate predictions of the positions of the planets than the models of Copernicus and Tycho did. The improved accuracy of the results gave a lot of support for the heliocentric model, and hence also (after the fact) to the model of Copernicus but not that of Tycho.
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