RNA viruses may be monopartite (all genes on one strand), multipartite (two or more strands packaged separately) or segmented (two or more strands packaged together). In this article, we consider competition between a complete monopartite virus, A, and two defective viruses, D and E, that have complementary genes. We use stochastic models that follow gene translation, RNA replication, virus assembly, and transmission between cells. D and E multiply faster than A when stored in the same host as A or when together in the same host, but they cannot multiply alone. D and E strands are packaged as separate particles unless a mechanism evolves that allows assembly of D + E segmented particles. We show that if defective viruses assemble rapidly into separate particles, the formation of segmented particles is selected against. In this case, D and E spread as parasites of A, and the bipartite D + E combination eliminates A if the transmissibility is high. Alternatively, if defective strands do not assemble rapidly into separate particles, then a mechanism for assembly of segmented particles is selected for. In this case, the segmented virus can eliminate A if transmissibility is high. Conditions of excess protein resources favor bipartite viruses, while conditions of excess RNA resources favor segmented viruses. We study the error threshold behavior that arises when deleterious mutations are introduced. Relative to bipartite and segmented viruses, deleterious mutations favor monopartite viruses. A monopartite virus can give rise to either a bipartite or a segmented virus, but it is unlikely that both will originate from the same virus.