We report the results of a series of 1 μs-long explicit-solvent molecular dynamics (MD) simulations performed to compare the free energies of stacking (ΔGstack) of all possible combinations of DNA and RNA nucleoside (NS) pairs and dinucleoside-monophosphates (DNMPs). For both NS-pairs and DNMPs we show that the computed stacking free energies are in reasonable qualitative agreement with experimental measurements, and appear to provide the closest correspondence with experiment yet found among computational studies; in all cases, however, the computed stacking free energies are too favorable relative to experiment. Comparisons of NS-pair systems indicate that stacking interactions are very similar in RNA and DNA systems except when a thymine or uracil base is involved: the presence of a thymine base favors stacking by ~0.3 kcal/mol relative to a uracil base. One exception is found in the self-stacking of cytidines, which are found to be significantly more favorable for the DNA form; an analysis of the rotational orientations sampled during stacking events suggests that this is likely to be due to more favorable sugar-sugar interactions in stacked complexes of deoxycytidines. Comparisons of the DNMP systems indicate that stacking interactions are more favorable in RNA than in DNA except, again, when thymine or uracil bases are involved. Finally, additional simulations performed using a previous generation of the AMBER force field – in which the description of glycosidic bond rotations was less than optimal – produce computed stacking free energies that are in poorer agreement with experimental data. Overall, the simulations provide a comprehensive view of stacking thermodynamics in NS pairs and in DNMPs as predicted by a state-of-the-art MD force field.