Charge-transfer (CT) states are of special interest in photochemical research because they can facilitate chemical reactions through the rearrangement of electrons and subsequently chemical bonds in a molecular system. Of particular importance to this research is the transfer of electrons between π-stacked nucleobases in DNA because they play an important role in its photophysics and photochemistry. Computational methods are paramount for the study of CT states because of the current inability of experimental methods to easily detect such states. However, many ab-initio wavefunction-based and density functional theory (DFT) methods fail to accurately describe these CT states. Here, we benchmark how 40 different quantum mechanical methods describe the excited states of a guanine-thymine π-stacked nucleobase dimer system, both in 5'-TG-3' and 5'-GT-3' conformations. We find that the distance between the nucleobases plays a major role in the energy of the CT state and in the difference of the dipole moments between the CT and ground state. There is a larger range of values (and errors) for the energies of CT states compared to those of states localized on one nucleobase. Wavefunction-based methods have similar errors for the CT and localized valence states, while DFT methods are very sensitive to the amount of Hartree-Fock exchange. Long-range-corrected functionals with a careful balance of the Hartree-Fock exchange included can predict very accurate CT states and a balanced description with the localized states.