Many species that compete for space live on heterogeneous landscapes and interact at local scales. The quality, amount, and structure of landscapes may have considerable impact on the ability of species to compete or coexist, yet basic models of space competition do not include that level of detail. We model space competition between two species with positive feedback through recruitment facilitation, which creates the potential for alternative stable states to occur. We compare the predictions of a spatially implicit model with a simulation model that includes explicit space and landscape structure. We create structured landscapes in which we specify the amount of habitat and degree of fragmentation and ask how landscape structure, dispersal strategy, and scale affect the presence of alternative stable states, or bistability. We find that structured landscapes can reduce the range of parameter values that lead to bistability in our model, but they do not eliminate bistability. The type of landscape and the dispersal distance for each species also influence the amount of environmental change needed for abrupt community shifts to occur. Coexistence of the two competitors is possible under certain conditions when connectivity is low. Consequently, landscape structure may lead to considerable disparity between the predictions of simple models and actual dynamics on complex landscapes during environmental change.