Using molecular simulation, we shed light on the coupling between the two nonequilibrium processes of demixing and crystallization in mixtures of fully miscible, size-matched, liquid metals. We show that the competition between these processes has a strong impact on the crystallization pathway, leading to the formation of crystal nuclei with large excesses (up to 95%) in the component of higher cohesive energy, and resulting in increases of more than 30% in the free energy barrier of nucleation. The competition between demixing and crystallization goes on to impact the growth process, as shown by the large variations in composition observed at the surface and inside the growing crystallite.