Genomic phenotypes, such as DNA methylation and chromatin accessibility, can be used to characterize the transcriptional and regulatory activity of DNA within a cell. Recent technological advances have made it possible to measure such phenotypes very densely. This density often results in spatial structure, in the sense that measurements at nearby sites are very similar. In this article, we consider the task of comparing genomic phenotypes across experimental conditions, cell types, or disease subgroups. We propose a new method, Joint Adaptive Differential Estimation (JADE), which leverages the spatial structure inherent to genomic phenotypes. JADE simultaneously estimates smooth underlying group average genomic phenotype profiles and detects regions in which the average profile differs between groups. We evaluate JADE’s performance in several biologically plausible simulation settings. We also consider an application to the detection of regions with differential methylation between mature skeletal muscle cells, myotubes, and myoblasts.