We report the results of a systematic comparison between the vertically averaged model and the vertically explicit model of steady state, Keplerian, optically thick α-discs. The simulations have concerned discs currently found in three different systems: dwarf novae, young stellar objects and active galactic nuclei. In each case, we have explored four decades of accretion rates and almost the whole disc area (except the narrow region where the vertically averaged model has degenerate solutions). We find that the one layer approach gives a remarkably good estimate of the main physical quantities in the disc, and specially the temperature at the equatorial plane which is accurate to within 30% for cases considered. The major deviations (by a factor ) are observed on the disc half-thickness. The sensitivity of the results to the α-parameter value has been tested for and appears to be weak. This study suggests that the "precision"of the vertically averaged model which is easy to implement should be sufficient in practice for many astrophysical applications.