Competition can result in evolutionary changes to coexistence between competitors but there are no theoretical models that predict how the components of coexistence change during this eco-evolutionary process. Here we study the evolution of the coexistence components, niche overlap and competitive differences, in a two-species eco-evolutionary model based on consumer–resource interactions and quantitative genetic inheritance. Species evolve along a one-dimensional trait axis that allows for changes in both niche position and species intrinsic growth rates. There are three main results. First, the breadth of the environment has a strong effect on the dynamics, with broader environments leading to reduced niche overlap and enhanced coexistence. Second, coexistence often involves a reduction in niche overlap while competitive differences stay relatively constant or vice versa; in general changes in competitive differences maintain coexistence only when niche overlap remains constant. Large simultaneous changes in niche overlap and competitive difference often result in one of the species being excluded. Third, provided that the species evolve to a state where they coexist, the final niche overlap and competitive difference values are independent of the system’s initial state, although they do depend on the model’s parameters. The model suggests that evolution is often a destructive force for coexistence due to evolutionary changes in competitive differences, a finding that expands the paradox of diversity maintenance.