OH(OD) quantum state populations, rovibrational quantum state-resolved center-of-mass angular scattering distributions, and H-2(HD) coproduct internal energy release distributions have been determined for the hot H atom reactions with H2O and D2O at mean collision energies close to 1.4 eV. The experiments employ pulsed laser photolysis coupled with polarized Doppler-resolved laser induced fluorescence detection of the radical products. The OH((2)Pi (1/2),v'=0,N'=1,A') and OD((2)Pi (1/2),v(')=0,N-'=1,A(')) angular distributions generated by the two isotopic reactions are quite distinct: that for the reaction with H2O shows intensity over a wide range of center-of-mass scattering angles, and peaks in the sideways direction, while the state-resolved angular distribution for the reaction with D2O displays more scattering in the backward hemisphere. For higher OH(OD) angular momentum states the differences in the angular distributions for the two reactions are less marked, with both systems showing a slight preference for backward scattering. The kinetic energy release distributions are insensitive to OH(OD) quantum state and to isotopic substitution, and reveal that the H-2(HD) coproducts are born internally cold at 1.4 eV. OH(OD) quantum state averaged energy disposals in the two reactions are also presented. The new experiments provide detailed mechanistic information about the two reactions and clarify the dominant sources of product OH(OD) rotational excitation. Current theoretical understanding of the reaction is critically assessed.