We use a semi-analytic model of galaxy formation to compare the predictions of two quenching scenarios: halo quenching and black hole (BH) quenching. After calibrating both models so that they fit the mass function of galaxies, BH quenching is in better agreement with the fraction of passive galaxies as a function of stellar mass M_* and with the galaxy morphological distribution on a star formation rate versus M_* diagram. Besides this main finding, there are two other results from this research. First, a successful BH-quenching model requires that minor mergers contribute to the growth of supermassive BHs. If galaxies that reach high M_* through repeated minor mergers are not quenched, there are too many blue galaxies at high masses. Second, the growth of BHs in mergers must become less efficient at low masses in order to reproduce the M_BH-M_* relation and the passive fraction as a function of M_*, in agreement with the idea that supernovae prevent efficient BH growth in systems with low escape speeds. Our findings are consistent with a quasar-feedback scenario in which BHs grow until they are massive enough to blow away the cold gas in their host galaxies and to heat the hot circumgalactic medium to such high entropy that its cooling time becomes long. They also support the notion that quenching and maintenance correspond to different feedback regimes.