In this work, the radiation response of bulk GaN and Ga2O3 materials exposed to ground-level neutrons is studied by Geant4 numerical simulation, considering the whole atmospheric neutron spectrum at sea level, from thermal to high energies (GeV). The response of the two materials is compared in terms of the number and type of interactions and the nature of the secondary products produced, particularly in nuclear reactions. Our results highlight the importance of 14N(n,p)14C neutron capture in the radiation response of GaN, leading to large differences in the behavior of the two materials in terms of susceptibility to thermal and intermediate-energy (below 1 MeV) neutrons.