The dynamics of H-atom abstraction reactions of Cl atoms with CH3Cl and CH3Br have been studied using velocity map imaging to obtain center-of-mass frame differential cross sections for HCl formed in its vibrational ground state and rotational levels with J = 2-5. The HCl products are preferentially backward scattered in both reactions, with broad angular distributions of velocities that extend to sideways and forward scatter, and which show almost no variation with J. The products are formed with a wide range of kinetic energies, and the mean fractions of the total available energy becoming product translational energy are 0.25 and 0.23 for the respective reactions. The CH2Cl and CH2Br are formed with considerable internal excitation, estimated to correspond, on average, to fractions of the total available energy of 0.69 and 0.72, respectively. The scattering dynamics are interpreted with the aid of ab initio calculations of the minimum energy pathways for the two reactions, which exhibit low barriers late on the reaction coordinate.