For the OH + CH4/CD4 hydrogen abstraction reactions, the methyl radical (CH3 and CD3) product translational distributions and the water (H2O and HOD) product vibrational distributions experimentally reported by Liu's group are reproduced by quasi-classical trajectory (QCT) calculations on an analytical full-dimensional potential energy surface when a quantum spirit is included in the analysis. Our simulations correctly predict: (i) the vibrational excitation of the water product, (ii) the inversion of the water vibrational population, and (iii) the propensity of transfer from reactant kinetic energy to product translational energy. These reactions therefore present a marked isotopic effect. In addition, the water product vibrational distributions for the OH/OD + CH4 reactions agree reasonably well with Butkovskaya and Setser's experiments for a similar alkane reaction. The theory/experiment agreement is better for the HOD than for the H2O product due to the mode coupling in the H2O molecule, which is absent in the HOD stretching modes, which show a more "local" character. In summary, for polyatomic systems with many degrees of freedom (15 in the present reaction), QCT calculations analyzed with a quantum spirit represent a useful alternative to quantum scattering methods.