In two recent papers, the mesoscale model Meso-NH, jointly with the Astro-Meso-NH package, has been validated at Dome C, Antarctica, for the characterization of optical turbulence. It has been shown that the meteorological parameters (temperature and wind speed, on which the optical turbulence depends) as well as the C2N profiles above Dome C were correctly reproduced statistically. The three most important derived parameters that characterize the optical turbulence above the Internal Antarctic Plateau – the surface-layer thickness, the seeing in the free atmosphere and the seeing in the total atmosphere – were shown to be in very good agreement with observations. Validation of C2N has been performed using all the measurements of the optical turbulence vertical distribution obtained in winter so far. In this paper, in order to investigate the ability of the model to discriminate between different turbulence conditions for site testing, we extend the study to two other potential astronomical sites in Antarctica: Dome A and South Pole, which we expect to be characterized by different turbulence conditions. The optical turbulence has been calculated above these two sites for the same 15 nights studied for Dome C and a comparison between the three sites has been performed. The ability of the Meso-NH model to discriminate between different types of optical turbulence behaviour is confirmed, and it is evident that the three sites considered have different characteristics as regards the seeing and the surface-layer thickness.