Extended full-dimensional quasiclassical trajectory calculations have been performed for the H(a)H(b) (v(ab) = 10, 11, 12, 13, 14, j(ab) = 0) + H(c)H(d) (v(cd) = 0, j(cd) = 0) collisions at values of the translational energy ranging from threshold to 1.5 eV and values of the total angular momentum quantum number J varying from zero to very large ones. Collision-induced dissociation, four-center exchange reaction, and single exchange process probabilities have been calculated. Full-dimensional classical calculations were found to reproduce well the corresponding (J = 0) quantum results, including the thresholds. In contrast, the agreement of full-dimensional classical calculations with the corresponding both quantum and classical reduced dimensionality ones was found to be poor. The effect of varying J on the efficiency of the various processes has also been investigated. Four-center reactions were found to be favored by low values of J, whereas dissociation processes were found to be favored by higher values of J, as expected from the fact that energy exchange takes place at longer range than mass exchange. To evaluate to what extent the J = 0 full-dimensional calculations represent the unconstrained dynamics of the system, J-shift model classical results were compared with the all-J ones. Product vibrational distributions for both partially dissociative and exchange processes were also found to depend significantly on the value of J.