Thermal rate constants and several kinetic isotope effects were evaluated for the OH + CH4 hydrogen abstraction reaction using two kinetics approaches, ring polymer molecular dynamics (RPMD) and variational transition state theory with multidimensional tunneling (VTST/MT), based on a refined full-dimensional analytical potential energy surface, PES-2014, in the temperature range 200-2000 K. For the OH + CH4 reaction, at low temperatures, T = 200 K, where the quantum tunneling effect is more important, RPMD overestimates the experimental rate constants due to problems associated with PES-2014 in the deep tunneling regime and to the known overestimation of this method in asymmetric reactions, while VTST/MT presents a better agreement, differences about 10%, due to compensation of several factors, inaccuracy of PES-2014, and ignoring anharmonicity. In the opposite extreme, T = 1000 K, recrossing effects play the main role, and the difference between both methods is now smaller, by a factor of 1.5. Given that RPMD results are exact in the high-temperature limit, the discrepancy is due to the approaches used in the VTST/MT method, such as ignoring the anharmonicity of the lowest vibrational frequencies along the reaction path, which leads to an incorrect location of the dividing surface between reactants and products. The analysis of several kinetic isotope effects, OH + CD4, OD + CH4, and OH + (CH4)-C-12/(CH4)-C-13, sheds light on these problems and confirms the previous conclusions. In general, the agreement with the available experimental data is reasonable, although discrepancies persist, and they have been analyzed as a function of the many factors affecting the theoretical calculations: limitations of the kinetics methods and of the potential energy surface, and uncertainties in the experimental measurements. Finally, in the absence of full-dimensional quantum mechanics calculations, this study represents an additional step in understanding this seven-atom hydrogen abstraction reaction.