The dynamics of the deuteron-proton exchange D(+) + H(2) → HD + H(+) reaction on its ground 1(1)A' potential energy surface has been the subject of a theoretical study for collision energies below 1.5 eV. The results obtained with three theoretical approaches: quasi-classical trajectory (QCT), statistical quasi-classical trajectory (SQCT), and accurate time-independent quantum mechanical (QM) calculations are compared in the range of collision energies from 5 meV to 0.2 eV. The QM calculations included all total angular momentum quantum numbers, J, up to J(max) ≈ 40 and all the Coriolis couplings. For higher collision energies, the comparison was restricted to the QCT and SQCT results given the enormous computational cost implied in the QM calculations. Reaction cross sections as a function of collision energy (excitation functions) for various initial rovibrational states have been determined and compared with the corresponding results for the endothermic H(+) + D(2) → HD + D(+) isotopic variant. The excitation function for the title reaction decays monotonically with collision energy as expected for an exothermic reaction without a barrier, in contrast to the behaviour observed in the mentioned H(+) + D(2) (v = 0, j ≤ 3). Reaction probabilities as a function of J (opacity functions) at several collision energies calculated with the different approaches were also examined and important differences between them were found. The effect of using the gaussian binning procedure that preserves, to a large extent, the zero point energy, as compared to the standard histogram binning in the QCT calculations, is also examined. At low collision energy, the best agreement with the accurate QM results is given by the SQCT data, although they tend to overestimate the reactivity. The deviations from the statistical behaviour of the QCT data at higher energies are remarkable. Nevertheless, on the whole, the title reaction can be deemed more statistical than the H(+) + D(2) reaction.