For many species, the outcome of competition for space in homogeneous habitats depends upon relative rates of growth and overgrowth. Size dependence in competition occurs when this balance shifts due to the growth of one or both species. For example, the ability of coral to compete with certain species of crustose coralline algae (CCA) may depend on whether coral colonies are large enough to avoid being overgrown. Spatially implicit models suggest size refuges from competition can improve the persistence of species with a vulnerable life stage. We use spatially explicit simulation models to explore size dependence in competition between coral and competitively dominant CCA in well lit habitat. We determine what conditions allow coral to use size refuges and whether refuges improve the recovery of coral after disturbance. Local interactions in explicit space prevent the maturation of coral into size refuges unless coral grows more rapidly than CCA or coral colonies are allowed to fuse, and mortality mechanisms can limit long-term persistence even if the refuge is achieved. We contrast results with analogous differential equation models, with and without an explicit maturation delay, to demonstrate how the predicted outcome of competition is frequently reversed when local interactions and individual-based dynamics are included in models of size-dependent competition.