Combined analyses of the surface elemental composition and mineralogy of Vesta and Ceres provide insights into their interior evolution, crustal formation, and regolith processes. Compositional data acquired by Dawn's Visible to Infrared Mapping Spectrometer (VIR) and Gamma Ray and Neutron Detector (GRaND) are sensitive to different depths and spatial scales. To compare these data sets, high-resolution maps of absorption band strengths from VIR are degraded to the broad spatial scales sampled by GRaND using a physics-based smoothing algorithm that accounts for the shape and topography of Vesta and Ceres. On Vesta, the distributions of elemental hydrogen and hydroxyl are similar, which implies that hydrogen is primarily in the form of hydroxyl, likely as phyllosilicates delivered by the infall of carbonaceous chondrite impactors. Small differences in the spatial patterns of hydroxyl and hydrogen imply that hydrogen is layered in some locations. In Vesta's dark hemisphere, hydrogen deposits are more extensive than hydroxyl, which indicates higher concentrations of hydrated minerals at depth. In contrast, the distributions of elemental hydrogen and hydrogen-bearing species (OH and NH4+) on Ceres are dissimilar. High concentrations of hydrogen in the Ceres’ polar regions (approaching 30 wt.% equivalent H2O) indicate the presence of subsurface ice as predicted by ice stability theory. The concentration of iron follows a water-dilution trend when plotted as a function of regolith hydrogen content, consistent with the presence of subsurface water ice. The VIR and GRaND data jointly constrain aspects of Ceres’ surface chemistry and evolution. GRaND iron measurements place a firm upper bound on magnetite content, which supports graphitized carbon as an alternative to magnetite as a darkening agent. Lower-bounds on the concentration of carbon in carbonates implied by VIR, together with the ratio of carbonates to organics in carbonaceous chondrite meteorite analogs suggest high concentrations of carbon within Ceres’ regolith. GRaND neutron measurements permit elevated carbon concentrations, equal to or in excess of that found in CI chondrites (greater than a few wt.%). Organic matter, detected by VIR at Ernutet crater, might be widespread and may have been converted to graphite, e.g. via UV exposure, elsewhere on the surface. Furthermore, elevated concentrations of carbonaceous material can explain the difference between iron and hydrogen concentrations measured by GRaND and the CI carbonaceous chondrites, which are representative of the materials from which Ceres accreted. The elemental measurements indicate that ice and rock fractionated during Ceres’ evolution producing a crust that differs in composition from the whole body.