Both competition and predation are considered to have important effects on the maintenance of species diversity. However, these two interactions are viewed highly asymmetrically: competition for resources is commonly viewed as the primary interaction limiting species diversity, with predation potentially modifying what competition does. However, views by ecologists on this topic have ranged from the simplest view that predation generally promotes coexistence by reducing the intensity of competition, to more nuanced views where the effect of predation is seen as varying greatly with the circumstances. This asymmetrical perspective on the interaction between predation and competition has persisted despite the emphasis by Holt and others that sharing a predator leads to mutually negative indirect interactions between prey species analogous to exploitative competition (termed "apparent competition"), and can equally well limit diversity. We develop three trophic-level models of interacting species which show that, at the core, competition for resources and predation are equally able to limit diversity or promote diversity. Diversity is promoted when prey species differ in which predators attack them, or in which resources they depend on most. Diversity is limited by similarity in these respects. In any given situation, either predation or competition may be stronger, and the tendency of the stronger interaction to promote or limit diversity prevails. When the two are similarly strong, they jointly promote or limit diversity. These results suggest a multitrophic level perspective on maintenance of species diversity where trophic cascades have an important role in patterns of species diversity in ecological communities.