We compare the ratios of the Frank elasticity coefficients calculated within a recently developed molecular theory, based on the approximation of perfect local orientational order, with the results of computer simulations presented by Frenkel, Allen, Tjipto-Margo and Evans for fluids of hard prolate and oblate ellipsoids. Good agreement is found for high densities, which correspond to those of thermotropic nematics, and for realistic values of the axial ratio. By constrast, at lower densities the approximation of perfect local order appears to be inadequate and the results of computer simulations follow the predictions of mean-field-like theories.