Stimulated by recent experiments [B. E. Rocher-Casterline, L. C. Ch'ng, A. K. Mollner, and H. Reisler, J. Chem. Phys. 134, 211101 (2011)], we report quasiclassical trajectory calculations of the dissociation dynamics of the water dimer, (H(2)O)(2) (and also (D(2)O)(2)) using a full-dimensional ab initio potential energy surface. The dissociation is initiated by exciting the H-bonded OH(OD)-stretch, as done experimentally for (H(2)O)(2). Normal mode analysis of the fragment pairs is done and the correlated vibrational populations are obtained by (a) standard histogram binning (HB), (b) harmonic normal-mode energy-based Gaussian binning (GB), and (c) a modified version of (b) using accurate vibrational energies obtained in the Cartesian space. We show that HB allows opening quantum mechanically closed states, whereas GB, especially via (c), gives physically correct results. Dissociation of both (H(2)O)(2) and (D(2)O)(2) mainly produces either fragment in the bending excited (010) state. The H(2)O(J) and D(2)O(J) rotational distributions are similar, peaking at J = 3-5. The computations do not show significant difference between the ro-vibrational distributions of the donor and acceptor fragments. Diffusion Monte Carlo computations are performed for (D(2)O)(2) providing an accurate zero-point energy of 7247 cm(-1), and thus, a benchmark D(0) of 1244 ± 5 cm(-1).