The quasiclassical trajectory method has been applied to the calculation of cross sections and rate constants for the H + D-2 --> HD +D reaction on three ab initio potential energy surfaces. The results include state-selected cross sections for the reaction with D-2(v=0j=0-9) and D-2(v=1j=0) and thermal rate constants in the 200-1500 K temperature range. A global good agreement is found between the present results and those from experiment and from approximate quantum mechanical calculations. This agreement is particularly good between 200 and 900 K. At higher temperatures, the quasiclassical rate constants deviate gradually toward lower values. A detailed comparison is performed between the reactivity of this isotopic variant and that of D + H-2. Special attention is paid to the effect of rotational excitation on reactivity, which is opposite for the two isotopomers, and to the microscopic dynamics responsible for the observed ratio of thermal rate constants and cross sections. In particular, the larger reaction cross section of D + H-2 as compared with H + D-2 is found to be caused by the more efficient transfer of collision energy from the heavier D atom to the molecular bond of the lighter H-2 molecule. These findings can be rationalized with simple dynamical models.