The nondestructive characterization of nanoscale devices, such as those based on semiconductor nanowires, in terms of functional potentials is crucial for correlating device properties with their morphological/materials features, as well as for precisely tuning and optimizing their growth process. Electron holographic tomography (EHT) has been used in the past to reconstruct the total potential distribution in three-dimension but hitherto lacked a quantitative approach to separate potential variations due to chemical composition changes (mean inner potential, MIP) and space charges. In this Letter, we combine and correlate EHT and high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) tomography on an individual «111» oriented GaAs-AlGaAs core-multishell nanowire (NW). We obtain excellent agreement between both methods in terms of the determined Al concentration within the AlGaAs shell, as well as thickness variations of the few nanometer thin GaAs shell acting as quantum well tube. Subtracting the MIP determined from the STEM tomogram, enables us to observe functional potentials at the NW surfaces and at the Au-NW interface, both ascribed to surface/interface pinning of the semiconductor Fermi level.