A central challenge for sustainable development is how societies are to avoid, minimize or address impacts from anthropogenic climate change. However, competing perspectives on “what should be sustained” lead to widely different understandings of what mitigation, adaptation and loss and damage entail and how best to approach them. We provide a novel conceptual and empirical comparison of two contrasting sustainable development-based approaches to the study of impacts from climate-related extreme events: Capital Theory and capability-based Human Development. We use our analysis of immediate residential property value and housing capacity impacts caused by Hurricane Michael in Gulf County, Florida, to demonstrate how the sustainable development theory used to assess and interpret impacts greatly affects the identification of whom and where is objectively “most impacted.” Through a comparison of the two approaches, we identify relative advantages and disadvantages, emphasizing that while both provide coherent, comprehensive, and integrative approaches to climate-related impact assessment, the capability approach is much less likely to lead researchers and practitioners to overlook the most disadvantaged communities when compared to Capital Theory.