Projections of future climate are uncertain owing to three primary factors: scenario uncertainty, model or response uncertainty, and internal variability. Several recent studies have performed uncertainty decompositions to shed light on the relative importance of each of these factors in driving projection spread. However, these studies typically rely on coarse-resolution and potentially biased climate model outputs. Thus, an outstanding research question is to what extent downscaling and bias-correction alter the uncertainty decomposition of future climate projections. In this work, we perform a simple variance decomposition on an ensemble of statistically downscaled and bias-corrected climate models as well as on the same set of native models from the Coupled Model Intercomparison Project Phase 6 (CMIP6). Focusing on temperature and precipitation, we analyze long-term indicators of climate change and several indices of climate extremes. Our results exhibit strong spatial dependencies, but in general we find that downscaling and bias-correction can considerably alter the relative contribution of uncertainty sources at local scales. In keeping with recent literature, we find an important role for internal variability in projections of climate extremes, suggesting that provisioners of downscaled and bias-corrected ensembles may wish to consider sampling several initial condition variants from the parent models in order to guard against overconfidence. Our results can also provide guidance for impacts modelers and decision-makers regarding the use of downscaled and bias-corrected climate information for local-scale analyses.