<p>This paper investigates a reaction-diffusion chemostat model involving two species that compete for a single limited resource. The study focuses on the combined effects of diffusion and growth on the extinction and survival of species under different competitive scenarios. For the weak-strong competition case, there exist two critical diffusion rates, which classify the global dynamics of this system into two outcomes: (i) persistence of the species with a strong growth capacity; (ii) extinction of both species. For the evenly matched competition case, the analysis reveals that the existence of two critical curves associated with growth rates will separate competition outcomes into competitive exclusion and coexistence. The study further provides the numerical approaches that not only confirm the theoretical results, but also illustrate the geometry of the critical curves within the diffusion-growth rates plane. These theoretical and numerical results contribute valuable insights into the dynamics of species competition in resource-limited environments.</p>