Quantum mechanical (QM) and quasi-classical trajectory (QCT) calculations have been performed for the Cl+H-2, Cl+D-2, Cl+HD --> HCl(DCl)+D(H) reactions in order to determine integral cross sections as a function of collision energy and for different reagent rotational quantum numbers using the recent ab initio BW2 potential energy surface (PES) by Bian and Werner [J. Chem. Phys. 112, 220 (2000)]. The results are compared with experimental data obtained by using the Doppler-selected time-of-flight technique. It has been found theoretically by both the QM and QCT methods that reagent rotation enhances reactivity in agreement with experiment. The QM results are found to be in quantitative agreement with the experimental excitation functions for the Cl+p-H-2 and Cl+n-H-2 reactions, whereas those obtained quasi-classically fail to reproduce the experimental data. These results are in strong contrast with those reported on the previous G3 PES, in which QM and QCT calculations predicted that reactivity decreases with reagent rotation. The intermolecular isotope effect, i.e., the ratio between the cross sections of the Cl+n-H-2 and Cl+n-D-2 reactions, Gamma (inter)(Cl+n-H-2/Cl+n-D-2), predicted by QM calculations on the BW2 surface is notably larger than that obtained experimentally.