Metal nanoparticles (MNPs) labeled with radioisotopes (RIs) are utilized as radio-enhancers due to their ability to amplify the radiation dose in their immediate vicinity. A thorough understanding of nanoscale dosimetry around MNPs enables their effective application in radiotherapy. However, nanoscale dosimetry around MNPs still requires further investigation. This study aims to provide insight into the radio-enhancement effects of MNPs by elucidating nanoscale dosimetry surrounding MNPs labeled with Auger-emitting RIs. We particularly focus on distinguishing the respective dose contributions of photons and electrons emitted by Auger-emitting RIs in the context of dose enhancement. A 50nm diameter NP of silver (Ag) core and gold (Au) shell (Ag@Au NP) was assumed to emit mono-energetic electrons and photons (3, 5, 10, 20, and 30keV), or the energy spectrum corresponding to one of three Auger-emitting RIs (103Pd, 125I, and 131Cs) from the Ag core. Nanoscale radial dose distributions around a single radioactive Ag@Au NP were evaluated in spherical shells of water. Monte Carlo simulations were conducted using single-event and track structure transport methods implemented in MCNP6.2 and Geant4-DNA-Au physics, respectively. To evaluate the extent of radio-enhancement by the Ag@Au NP, two scenarios were considered: Ag@Au NPs (Au shell included) and Ag@water NPs (Au shell replaced by water). The radial doses of 10, 20, and 30keV electrons estimated by both codes were comparable. However, the radial doses of 3 and 5keV electrons by MCNP6.2 were much larger near the NP surface than those by Geant4. There was a dose enhancement of a few % to tens % by the Au shell in the region of the NP surface to 10µm, depending on the electron energy. The radial doses of photons with the Au shell were higher up to their secondary electron ranges than those without the Au shell. The maximum dose enhancement factor of photons occurred at 20keV and was 63.4 by MCNP6.2 and 50.5 by Geant4. The overall radial doses of electrons were 1-2 orders of magnitude larger than those of photons. As a result, in cases of RIs emitting both electrons and photons, the radial doses up to electron ranges were dominantly governed by electrons. The dose enhancement estimated by both codes for the RIs ranged from a few % except in the immediate vicinity of the NP surface. Given the dominant contribution of electrons to radial doses of MNP labeled with Auger-emitting RIs, physical dose enhancement expected by interactions with photons was hindered. Since there are no available RIs emitting exclusively photons, achieving enhanced physical doses within a cell through a combination of MNPs and RIs appears currently unattainable. The radial doses of photons near the NP surface exhibited considerable discrepancies between the codes, primarily attributed to low-energy electrons. The difference may arise from higher cross-sections of Au inelastic scattering in Geant4-DNA-Au compared to MCNP6.2.