Variational transition state theory (VTST) methods and quasiclassical trajectories (QCT) have been used to study the dynamics of the OH+H-2 reaction, along with the isotopic counterparts OD+H-2, OH+HD, OD+H-2, OD+D-2, and the reverse H+H2O -->H-2+OH reaction. Two new global analytical potential energy surfaces (PES) for H3O are employed, Wu, Schatz, Lendvay, Fang, Harding (WSLFH) and Ochoa, Clary (OC), both of which are based on high quality electronic structure calculations. Extensive comparisons with earlier results based on the Walch, Dunning, Schatz, Elgersma (WDSE) PES are also presented. The WSLFH PES surface, in combination with our best VTST estimate (ICVT/mu OMT), yields rate constants for OH+H-2 in quantitative agreement with experiment, while the OC PES yields somewhat less accurate results. The agreement with the OH+D-2 experimental rate constants is less quantitative, but the WSLFH PES rate constant agrees with experiment to within a factor of 2 at all temperatures for which there are measurements. The OH+HD, OD+H-2, and OD+D-2 WSLFH PES rate constants calculated at the ICVT/mu OMT level are in very good agreement with the less detailed experimental information that is available for these isotopes. The two surfaces give comparable predictions for the reverse H+H2O reaction at high temperatures, with deviations of less than 30%. This good agreement is maintained by the WSLFH PES at room temperature, while the OC PES predicts rate constants one order of magnitude larger than experiment. The QCT excitation functions for OH+H-2, OH+D-2, and OH+HD are well below experiment for both potentials, as was the case for earlier accurate quantum mechanical calculations that employed the WDSE PES. The WSLFH PES improves the agreement with the experimental vibrational state selected rate constants for the OH+H-2 reaction compared to the WDSE PES. OC is also less accurate and presents antithreshold behavior for H-2(v=1)+OH. H-2 and OH rotational excitation have opposing effects: while rotation in H-2 promotes reactivity, OH rotation impedes it. This impeding effect applies likewise to HD for high rotational excitation, explaining the selectivity toward HOH+D products in the OH+HD reaction.