We use the local density approximation of the density functional theory to perform a comparative analysis between the bonding interactions of the epitaxial graphene/SiC interface in the case of Si and C face growth [i.e. growth on the SiC(0001) and the surfaces respectively]. We argue that when the SiC substrate below the graphene films reconstructs with no additional adatoms, the observed electronic differences are the outcome of an interplay between and hybridization of the interface atoms. We find a strong preferential disposition towards an hybridization for the case of the C face, whereas towards the scheme for the Si face. Notwithstanding purely quantitative, this mismatch is important and reflects the strength of the bond in Si and C.