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Patterned vegetation is a characteristic feature of many dryland ecosystems. While plant densities on the ecosystem-wide scale are typically low, a spatial self-organisation principle leads to the occurrence of alternating patches of high biomass and patches of bare soil. Nevertheless, intraspecific competition dynamics other than competition for water over long spatial scales are commonly ignored in mathematical models for vegetation patterns. In this chapter, I address the impact of local intraspecific competition on a modelling framework for banded vegetation patterns. Firstly, I show that in the context of a single-species model, neglecting local intraspecific competition leads to an overestimation of a patterned ecosystem's resilience to increases in aridity. Secondly, in the context of a multispecies model, I argue that local intraspecific competition is a key element in the successful capture of species coexistence in model solutions representing a vegetation pattern. For both models, a detailed bifurcation analysis is presented to analyse the onset, existence and stability of patterns. Besides the strengths of local intraspecific competition, also the the difference between two species has a significant impact on the bifurcation structure, providing crucial insights into the complex ecosystem dynamics. Predictions on future ecosystem dynamics presented in this chapter, especially on pattern onset and pattern stability, can aid the development of conservation programs.