We present both the Born–Oppenheimer (BO) and the nonadiabatic (NA) conical-intersection quantum dynamics of the title reactions, (1) and (2), respectively. BO or NA calculations are carried out using adiabatic or diabatic electronic states, respectively, and we consider some vibrational (v 0 ) and rotational (j 0 ) states of O 2 , taking into account the Pauli principle. The results reflect the barrier or barrierless nature of reaction (1) or (2), respectively, and the former is, thus, much less reactive than the latter. Reaction (1) is direct and its probabilities and cross sections increase with the collision energy from a threshold value, are slightly affected by NA couplings only at high energies, increase with v 0 , and are essentially unchanged by j 0 . On the contrary, reaction (2) is indirect and its probabilities and cross sections decrease with the collision energy without any threshold, are significantly lowered by NA couplings at low energies, and decrease with both v 0 and j 0 .