Experimental and theoretical differential cross sections for the reactions between Cl atoms and two isotopic variants of molecular hydrogen (H-2 and D-2) are presented. The experimental results have been obtained by using the crossed molecular beam method with mass spectrometric detection. The theoretical results have been computed using both the quasiclassical trajectory and quantum mechanical (QM) methods. The potential energy surface employed for the calculations is the ab initio BW2 surface by Bian and Werner [J. Chem. Phys. 112, 220 (2000)]. The theoretical results have been directly compared to the experiments in the laboratory frame at a collision energy (E-c) of 4.25 and 5.85 kcal/mol for the Cl + H-2 reaction and of 4.9 and 6.3 kcal/mol for the Cl + D-2 reaction. The agreement between QM results and experiment is quite satisfactory for the Cl + D-2 reaction, especially for the low collision energy, while for Cl + H-2 is less good, especially when considering data at the lower E-c.