Vertical ionization energies of 9-H adenine and 9-methyl adenine have been calculated with the following, ab initio, electron propagator methods: the outer valence Green's function (OVGF), partial third-order theory (P3), and the third-order algebraic diagrammatic construction, or ADC(3). Basis set effects have been systematically examined. All methods predict near degeneracy in the pi(2)-n(1) and pi(3)-n(2) pairs of cationic, adenine final states and larger splittings of the corresponding, cationic states of 9-methyl adenine. P3 results for adenine predict the following order of the first six final states: pi(1), n(1), pi(2), n(2), pi(3), n(3). Coupled-cluster calculations on the first three cationic states of adenine confirm these predictions. OVGF and ADC(3) calculations reverse the order of the second and third states and of the fourth and fifth states. All results confirm previous interpretations of experiments in which the second and third spectral bands correspond to the aforementioned pairs of final states and disagree with a recent reassignment based on time-resolved photoelectron spectra. Lower ionization energies and larger splittings in the methylated molecule are interpreted in terms of phase relationships in the Dyson orbitals. ADC(3) results confirm the qualitative validity of the one-electron approximation for the first six final states of both molecules and disclose its inadequacies for higher ionization energies.