Single Photon Emission Computed Tomography (SPECT) is at present one of the major techniques for non-invasive diagnostics in nuclear medicine. Almost the whole clinical routine is based on collimated cameras, originally proposed by Anger. Due to the presence of mechanical collimation, detection efficiency and energy acceptance are limited by thesystem geometrical features. In order to overcome these limitations, the application of Compton cameras for SPECT is being investigated for several years. A Compton camera prototype is at present under development by our collaboration, for high energy gamma detection in ion beam therapy monitoring and nuclear medicine. We propose in this study to compare our detector to a commercial Anger device, the GE Healthcare Infinia system, through Monte Carlo simulations (GATE v7.1 and Geant4 9.6 respectively). Given the possible introduction of new radio-emitters at higher energiesintrinsically allowed by the Compton camera detection principle, the detectors are exposed to point-like sources at increasing primary gamma energies, from actual isotopes already proposed for SPECT applications. The detector performances are studied in terms of radial event distribution, detection efficiency and final image, obtained by gamma transmission analysis for the Anger system, and with an iterative LM-MLEM algorithm for the Compton reconstruction. The Compton camera prototype is also characterized in terms of rate of random coincidences and at different energy resolutions. Although the rate of random coincidences appears to be close to 50% at clinical source activities, preliminary results show for the Compton camera a detection efficiency increased of a factor greater than an order of magnitude, associated with an enhanced spatial resolution for energies beyond 500 keV. We discuss then the proven advantages of Compton camera application with particular focus on dose delivered to the patient, examination time and spatial uncertainties.