We present a detailed and quantitative comparison of the quantum mechanical (QM) and quasiclassical (QCT) descriptions of the stereodynamics of elementary chemical reactions. Analogous formulations of the QM and QCT k-k(')-j(') vector correlation in atom-diatom reactions have been derived and shown to be equivalent in the correspondence principle limit. The comparison between the results obtained from the application of the QM and QCT methodologies to the H + D-2(upsilon = 0, j = 0)--> HD(upsilon('),j(')) + D reaction at a collision energy of 1.29 eV renders an almost quantitative agreement.