A comparative post-Hartree-Fock study has been performed on cyclopropyl and oxiranyl radicals in order to ascertain the role of the oxygen atom in modifying the hyperfine structure and height of the barrier governing inversion at the radical center. The structural parameters and harmonic force fields obtained for the parent molecules using second-order many-body perturbation theory with a large basis set are in good agreement with experiment. The same approach points out significant distortions upon breaking of a CH bond and a larger pyramidality for the radical center in oxiranyl with respect to cyclopropyl. Also inversion barriers of both radicals are in remarkable agreement with experimental estimates. isotropic hyperfine parameters in good agreement with those obtained from electron spin resonance spectra can be computed only when using purposely tailored basis sets in the framework of a coupled cluster approach and taking into account vibrational averaging effects induced by the inversion motion. Interpretation of the results in terms of direct and spin polarization effects points out a number of general trends for germinal and vicinal atoms. Furthermore, it is well evidenced that replacement of a methylenic group by an oxygen atom modifies the hyperfine parameters through geometric rather than direct electronic effects.