Similarities and dissimilarities in the growth of diamond vs. c-BN, in the present series of investigations, have been studied using quantum mechanical calculations. Hydrogen species have been observed to be very effective in stabilising both types of compounds. Very large similarities have also been observed when considering the adsorption of various growth species to these materials. However, it was found necessary to avoid mixtures of B- and N-containing species in the gas phase during c-BN growth, since they should most probably result in a mixture of these species also on the (111) and (110) surfaces. In addition, a careful gas phase design was found necessary in order to avoid a preferential initial growth of h-BN. These theoretical results can be used as guide lines in striving towards a thin film deposition of cubic boron nitride using gentle CVD methods like atomic layer deposition.