Three-dimensional quantum scattering calculations have been carried out for the O(D-1) + N-2 --> O(P-3) + N-2 spin-forbidden electronic quenching process using a simplified collision model, in which only the lowest singlet surface and one triplet surface are taken into account. The standard close-coupling technique has been used to obtain nonadiabatic transition probabilities, and the coupled-state approximation was applied to calculate the total quenching cross section. Previously developed analytical potential energy surfaces and the spin-orbit coupling element have been employed. The results of the close-coupling calculations have been compared to the results of the quasiclassical trajectory surface hopping method. Two versions of the method have been used; one uses Tully's fewest switches algorithm, and the other is the hopping method of Preston and Tully. It has been found that both of the trajectory surface hopping methods give too large quenching probabilities compared to those of the quantum results, in which the quenching dynamics is exclusively resonance-dominated. Detailed analyses of the quantum results show that a curve crossing picture cannot be employed to describe the present nonadiabatic collision. The calculated quenching cross sections have been also compared to those of experimental data as well as previous theoretical results.