We analyse the phenomenological implications of the two-families scenario on the merger of compact stars. That scenario is based on the coexistence of both hadronic stars and strange quark stars. After discussing the classification of the possible mergers, we turn to detailed numerical simulations of the merger of two hadronic stars, i.e., first family stars in which delta resonances and hyperons are present, and we show results for the threshold mass of such binaries, for the mass dynamically ejected and the mass of the disk surrounding the post-merger object. We compare these results with those obtained within the one-family scenario and we conclude that relevant signatures of the two-families scenario can be suggested, in particular: the possibility of a rapid collapse to a black hole for masses even smaller than the ones associated to GW170817; during the first milliseconds, oscillations of the postmerger remnant at frequencies higher than the ones obtained in the one-family scenario; a large value of the mass dynamically ejected and a small mass of the disk, for binaries of low total mass. Finally, based on a population synthesis analysis, we present estimates of the number of mergers for: two hadronic stars; hadronic star - strange quark star; two strange quark stars. We show that for unequal mass systems and intermediate values of the total mass, the merger of a hadronic star and a strange quark star is very likely (GW170817 has a possible interpretation into this category of mergers). On the other hand, mergers of two strange quark stars are strongly suppressed.