The quasiclassical trajectory (QCT) method was used to study the dynamics of the OH(X (2) Pi) and OD(X (2) Pi)+HBr chemical reactions on an empirical potential energy surface (PES). The main emphasis in the calculation was the vibrational energy distributions of H2O (and HDO) and the magnitude and temperature dependence of the rate constant. However, this PES also serves as a generic model for the dynamics of direct H atom abstraction by OH radicals. Since this PES has no formal potential energy barrier, variational transition-state theory was used to obtain rate constants for comparison with the QCT calculations and experimental results. The parameters of the potential energy surface were adjusted to obtain better agreement with the experimentally measured fraction of H2O vibrational energy, [f(v)(H2O)]=0.6, without significantly changing the entrance channel. No isotope effect for the partition of energy to H2O vs HOD was found. Analysis of the trajectories indicates that the reactant OH(OD) bond is a spectator, until the system begins to traverse the exit channel, i.e., until H2O(HDO) starts to retreat from Br. The calculated average energy in the bending mode of H2O or HDO was lower than the experimental value, and the PES could not be adjusted in its present form to give a significantly larger fraction of energy to the bending mode. A nonlinear 1:2 resonance between the OH local mode and the bending mode was found to be the main mechanism leading to bending mode excitation for this PES. The QCT rate constant is larger than the value calculated by quantum methods or variational transition-state theory. This difference may arise from the absence of a zero point energy constraint in the QCT calculation.