Compton profiles, polarizabilities and related functions of diamond and cubic boron nitride have been investigated within the Hartree-Fock approximation and the density functional theory, calculated within the local density approximation and generalized gradient approximation, but without any explicit correlation correction for the Compton profiles. The correlation part already included in the standard uncorrected density functional theory is deduced from the comparison of the two types of calculation. The Compton profile and reciprocal-form-factor anisotropies, polarizability, dielectric constant and energy loss function of the two compounds are compared at the same level of accuracy. These properties are very close in spite of the rather different chemical bonds due to the charge transfer occurring in cubic boron nitride and gaps.