Terahertz emission spectroscopy of ultrathin multilayers of magnetic and heavy metals has recently attracted much interest. This method not only provides fundamental insights into photoinduced spin transport and spin-orbit interaction at highest frequencies but has also paved the way to applications such as efficient and ultrabroadband emitters of terahertz electromagnetic radiation. So far, predominantly standard ferromagnetic materials have been exploited. Here, by introducing a suitable figure of merit, we systematically compare the strength of terahertz emission from X/Pt bilayers with X being a complex ferro-, ferri- and antiferromagnetic metal, that is, dysprosium cobalt (DyCo$_5$), gadolinium iron (Gd$_{24}$Fe$_{76}$), Magnetite (Fe$_3$O$_4$) and iron rhodium (FeRh). We find that the performance in terms of spin-current generation not only depends on the spin polarization of the magnets conduction electrons but also on the specific interface conditions, thereby suggesting terahertz emission spectroscopy to be a highly surface-sensitive technique. In general, our results are relevant for all applications that rely on the optical generation of ultrafast spin currents in spintronic metallic multilayers.