We present the results of a joint experimental and theoretical investigation of the reaction dynamics of the H+HD --> D+H-2 chemical reaction. The experiment was performed using a crossed molecular beam apparatus that employed the Rydberg-atom time-of-flight detection scheme for the product D atom. The photolysis of a HI precursor molecule produced a beam source of hot H atoms, which, when crossed with a cold HD beam, yielded two well-defined center-of-mass collision energies, E-C = 0.498 and 1.200 eV. The resolution of the experiment was sufficient to allow the measurement of the rovibrationally state-resolved differential cross section from the ground state of the HD reagent. The reaction was modeled theoretically using a converged coupled channel scattering calculation employing the BKMP2 potential energy surface: The S matrix was computed on a grid of 56 energies in the range E-C = 0.245-1.551 eV. It is found that the experimental and theoretical state-to-state differential cross sections are in quantitative agreement at the two experimental energies. The geometric phase, which was not included in the calculation, is apparently not required at the energies considered. The spin statistics for the two identical protons is observed to have a dramatic effect on the rotational distribution of H-2 products, giving rise to a saw-toothed distribution with odd-j' >even-j'. The differential cross section for several of the product states exhibited a dramatic forward peak that may be the signature of trapped quantum states near the saddle point. A detailed analysis of the reaction attributes is presented based on the energy dependence of the computed S matrix.