We use the volume-conserving deformed liquid drop model to perform a quantitative study of the experimentally observed strong predominance of prolate over oblate shapes of nuclei. Except for very light nuclei, the binding energy difference between both types of quadrupole deformation is given by almost equal contributions from the Coulomb and surface terms.
We perform an analysis using up-to-date experimental data for electric quadrupole moments and B(E2) transition probabilities and show that, for a significant number of well-deformed nuclei, the prolate-oblate difference in binding energy reaches values of the order of 500-800 keV, which are considerably higher than typical low-lying excitation energies for these nuclei.