Earth-abundant chalcogenide thin-film solar cells, in particular Cu2ZnSnS4 (CZTS), have recently attracted a lot of attention in the field of photovoltaics. Further increases in CZTS performance are challenging, in part because of defects caused by the chemical complexity of this quaternary material. Ternary copper chalcogenides, such as Cu2SnS3 and CuSbS2, are chemically simpler, but their performance is still lower than that of CZTS. Here, we compare the physical properties of the Cu-Sn-S and Cu-Sb-S material families using a high-throughput combinatorial approach, with particular focus on Cu2SnS3 and CuSbS2. We find that both materials have similar competing phases, but they differ significantly in terms of their structures, composition stability ranges, optical absorption, and electrical transport properties. The results of this study lead to the conclusion that CuSbS2, with lower conductivity and higher absorption, may be more promising for the development of Earth-abundant thin-film solar cells despite its layered structure and lower phase stability range.