The model of Nambu and Jona-Lasinio has been extensively used to model the possible occurrence of quark matter in the core of compact stars. While based entirely on similar physical assumptions, previous studies have been performed using a variety of model versions, differing in both the number of active quark flavors and the structure of the quark-quark interaction. We discuss the results of our systematic analysis, designed to clarify the role of the vector and instanton-induced interactions in determining the properties of hybrid stars. The results of our calculations, carried out using a state-of-the-art description of the hadronic phase, show that the instanton-induced interaction does not affect the stiffness of the quark matter equation of state, whereas the effect of the repulsive vector interaction is sizable. However, no values of the corresponding coupling constants allow for the formation of a stable core of quark matter.