Various processes can take place simultaneously in H2 + D2 collisions: four-center reaction yielding HD + HD, collision induced dissociation resulting in D2 + H + H or H2 + D + D, and single exchange reaction producing HD + H + D. The initial state selected time-dependent wave packet method was employed to study the H2 (v1 = high) + D2 (v2 = low) reaction on two realistic global potential energy surfaces (ASP and BMKP) within the reduced-dimensional (3D) and full-dimensional (6D) models. The role of both vibrationally excited and rotationally excited reagents was examined by varying the reagent initial vibrational and rotational states. The isotope substitution effects were investigated by substituting the collider D2 by H2 and HD. In addition, the 6D integral cross sections for the H2 + D2 reaction were calculated with and without the centrifugal sudden (CS) approximation by including all important K blocks and the accuracy of the CS approximation was discussed.