A multivariate statistical analysis of data measuring the optical and X-ray properties of the Einstein sample of early-type galaxies (Eskridge et al. 1995) showed that: 1) on average S0s have lower X-ray luminosity LX at fixed optical luminosity LB than do Es; 2) at fixed LB the X-ray brightest galaxies are also the roundest; this correlation holds for both morphological subsets of Es and S0s. We investigate whether a flat and partially rotationally supported galaxy is expected to host a different gas flow phase (and so a largely different amount of hot gas) with respect to a spherical pressure supported galaxy of the same LB. This is accomplished using the global energetic balance of the hot gas flows, and axisymmetric two-component galaxy models (Ciotti and Pellegrini 1995).