Various properties of two polymorphs of carbon, highly oriented pyrolytic graphite (HOPG) and diamond, were investigated at the ab initio level using different Hamiltonians with all-electron Gaussian-type functions (GTF) and projector augmented wave (PAW) basis sets. Their equilibrium lattice parameters, cohesive and interlayer interaction energies, band structures, vibrational frequencies, and elastic constants were evaluated. The calculations were performed at the Hartree–Fock, density functional theory (DFT), and hybrid (B3LYP and PBE0) levels. As regards DFT, the local density and generalized gradient (PBE and PBEsol) approximations were used. For GTF, the influence of the basis set superposition error (BSSE) was assessed. Since these approaches do not take dispersion interactions correctly into account, two different versions of Grimme’s dispersion correction, D2 and D3, were evaluated. The D2 and D3 corrections were reparameterized in order to reproduce the experimental structure of HOPG. For the properties depending on the description of the covalent bonds, such as the cohesive energy, C 11 and C 12, the dispersion corrections have a negligible influence. The best agreement is found for B3LYP-GTF-D3, PBE providing close results. For the properties depending on the description of the interaction between different layers, such as the interlayer interaction energies, C 33, and C 44, using the dispersion corrections improves the results. In general, D3 performs better than D2. PBE overall provides better results than the other functionals. As regards the basis sets, PAW describes the vibrational frequencies better than GTF due to the BSSE, whereas GTF provides a better description of the bandwidths and interband separations, elastic constants, and thermodynamical data. On the basis of the overall results, PBE-GTF-D3 appears to be a good compromise for an accurate description of the properties of graphite.