  We revisit three of the mathematical formalisms used to describe magnetized
quark matter in compact objects within the MIT and the Nambu-Jona-Lasinio
models and then compare their results. The tree formalisms are based on 1)
isotropic equations of state, 2) anisotropic equations of state with different
parallel and perpendicular pressures and 3) the assumption of a chaotic field
approximation that results in a truly isotropic equation of state. We have seen
that the magnetization obtained with both models is very different: while the
MIT model produces well-behaved curves that are always positive for large
magnetic fields, the NJL model yields a magnetization with lots of spikes and
negative values. This fact has strong consequences on the results based on the
existence of anisotropic equations of state. We have also seen that, while the
isotropic formalism results in maximum stellar masses that increase
considerably when the magnetic fields increase, maximum masses obtained with
the chaotic field approximation never vary more than 5.5$\%$. The effect of the
magnetic field on the radii is opposed in the MIT and NJL models: with both
formalisms, isotropic and chaotic field approximation, for a fixed mass, the
radii increase with the increase of the magnetic field in the MIT bag model and
decrease in the NJL, the radii of quark stars described by the NJL model being
smaller than the ones described by the MIT model.
