Targeted Auger emitters are being considered as a cancer treatment owing to the high linear energy transfer of Auger electrons. When targeted to cancers, this allows for a highly efficient treatment with a low risk of damage to surrounding healthy tissue. The purpose of this study was to determine the most DNA-damaging Auger emitters from a range of radionuclides, some of which are clinically utilised. A Monte Carlo method-based software (Geant4-DNA version 10.7) was used to determine the energy deposition and number of DNA double-strand breaks from Auger (and internal conversion) electrons imposed on a tetranucleosome. The Auger emitters, 119Sb and 103Pd, have similar or slightly greater damaging properties compared to 123I, 111In, and 89Zr. 193mPt demonstrated the greatest therapeutic potency. Whilst 125I was highly damaging, its relatively long half-life (60 days) makes it less desirable for clinical use. Geant4-DNA modelling identified the radionuclide 193mPt as being highly favourable for use in radiotherapy.