Graphitic (g)-CxNyHz has become a popular element in photocatalytic water splitting cells. Recently, the crystal structures of completely polymerized g-C3N4 and incompletely polymerized g-C6N9H3 crystals based on the triazine and heptazine monomers have been characterized. In this manuscript we evaluate the atomic and electronic nature of these structures using DFT. The study revealed strongly corrugated structures for the fully polymerized g-C3N4 and planar structures for the incompletely polymerized g-C6N9H3. The exciton binding energies of the heptazine-based structures are lower than that of their triazine-based analogues and lower for the completely polymerized structures than their incompletely polymerized analogues. The rather low dielectric constant and charge mobilities result in high exciton binding energies and hence low dissociation probabilities for these excitons. This confirms the necessity of a morphology inspired by bulk heterojunction architectures to ensure efficient charge carrier generation. The studied compounds can be considered intermediates between typical inorganic and organic semiconductors in terms of their photoabsorption properties.