The recombination reaction between gaseous and adsorbed hydrogen atoms on the Cu(111) surface is a paradigmatic system for studying the Eley−Rideal (ER) mechanism at the gas-surface interface. Theoretically, this system has been mostly studied by the highly efficient quasi-classical trajectory (QCT) method, whose validity has, however, not been tested against more rigorous quantum dynamics (QD) calculations in high dimensionality. Here, based on our recent development of a six-dimensional (6D) fully coupled quantum wave packet method for studying the ER reaction, we present a comparative study between QD and QCT calculations in the H(D)+D(H)/Cu(111) ER reaction. We find that quasi-classical results show a similar magnitude of total reactivity and qualitatively consistent vibrational and rotational state distributions as quantum ones. However, QCT to some extent overestimates the vibrational excitation compared to QD, presumably due to the unavoidable leakage of the zero-point energy of the adsorbate into the product. Additionally, vibrational state-specific internal energy distributions predicted by QCT and QD show more remarkable discrepancies for higher vibrational states. These results provide a reliable benchmark for the capability of the QCT method in studying ER reactions. By the comparison with experiments, it is also suggested that to more accurately describe the ER reaction, the current QD model requires further developments to incorporate the hot-atom reaction channel.