Independently, both droughts and heatwaves can induce severe impacts on human and natural systems. However, when these two climate extremes occur concurrently in a given region, their compound impacts are often more pronounced. With the improvement in both the spatiotemporal resolution and representation of complex climate processes in the global climate models (GCMs), they are increasingly used to study future changes in these extremes and associated regional impacts. However, GCM selection for such impact assessments is generally based on historical performance and/or future mean changes, without considering individual or compound extremes. In contrast, this study evaluates historical performance and projected changes in heatwaves, droughts, and compound heatwave-droughts using an ensemble of GCMs from the latest Phase 6 of Coupled Models Intercomparison Project at a regional scale across the conterminous United States. Additionally, we explore the inter-model differences in the projected changes that are associated with various characteristics of extremes and the choice of drought indices. Our analysis reveals considerable variation among the GCMs, as well as substantial differences in the projected changes based on the choice of drought indices and region of interest. For example, the projected increases in both the frequency and intensity of drought and associated compound extreme days, based on the standardized precipitation evapotranspiration index far exceed those derived from the standard precipitation index. Further, the largest changes in the frequency of compound extremes are projected over the Southwest, South Central, and parts of the Southeast while the smallest changes are projected over the Northeast. Overall, this study provides important insights for the interpretation and selection of GCMs for future assessment studies that are crucial for the development of regional adaptation strategies in the face of climate change.