Competition and predation are the most heavily investigated species interactions in ecology, dominating studies of species diversity maintenance. However, these two interactions are most commonly viewed highly asymmetrically. Competition for resources is seen as the primary interaction limiting diversity, with predation modifying what competition does, although theoretical models have long supported diverse views. Here we show, using a comprehensive three-trophic-level model, that competition and predation should be viewed symmetrically: these two interactions are equally able to either limit or promote diversity. Diversity maintenance requires within-species density feedback loops to be stronger than between-species feedback loops. We quantify the contributions of predation and competition to these loops in a simple, interpretable form, showing their equivalent potential to strengthen or weaken diversity maintenance. Moreover, we show that competition and predation can undermine each other, with the tendency of the stronger interaction to promote or limit diversity prevailing. The past failure to appreciate the symmetrical effects and interactions of competition and predation has unduly restricted diversity maintenance studies. A multitrophic perspective should be adopted to examine a greater variety of possible effects of predation than generally considered in the past. Conservation and management strategies need to be much more concerned with the implications of changes in the strengths of trophic interactions.