A detailed comparison of quasiclassical trajectory (QCT) and quantum mechanical (QM) reaction probabilities and differential cross sections fdr the H+D-2-->HD+D reaction at the collision energies of 0.54 and 1.29 eV has been carried out using the same potential energy surface. The theoretical simulation of the recently published experimental results is also reported. The comparisons made here demonstrate the level of agreement between QCT and QM approaches, as well as between theory and experiment for this reaction.