We develop stochastic spatial epidemic models with the competition of two pathogenic strains. The dynamics resulting from different approaches are examined using both non-spatial and spatially explicit models. Our results show that pair approximation, well-mixed ordinary differential equations (ODEs), Gillespie-algorithm-based simulations and spatially explicit models give similar qualitative results. In particular, the temporal evolution of the spatial model can be successfully approximated by pair equations. Simulation results obtained from the spatially explicit model show that, first, mutation plays a major role in multi-strain coexistence, second, mild virulence remarkably decreases the coexistence domain of the parameter space and, third, large-scale self-organized spatial patterns emerge for a wide range of transmission and virulence parameter values, where spatial self-organized clusters reveal a power law behavior within the coexistence domain.