The photochemistries of HCN and DCN at the H(D) Lyman-alpha wavelength have been reinvestigated using the technique of H(D) Rydberg atom time-of-flight spectroscopy, with angular resolution of the H/D atom signal about the polarization vector of the photolysis radiation. In the case of HCN photodissociation, the previous assignment of substantial branching to H+CN(A (2)Pi)(v=0) products is confirmed. Analysis of the profile taken under parallel polarization of the Lyman-alpha radiation relative to the time of flight axis reveals additional structure attributable both to a progression in CN(A) products with high rovibrational excitation (v=4-9, with N similar to 26-41, for all v), and to various rotationally excited levels associated with CN(B (2)Sigma(+))(v=0,1). From these various assignments an improved value for the dissociation energy, D-0(H-CN)=43 710 +/- 70 cm(-1), is obtained. The determined beta parameter, which is a measure of the angular part of the photofragment velocity distribution about the polarization vector of the photolysis radiation, shows an increasingly parallel distribution of H atom velocities with increasing CN internal energy. DCN photolysis at the D Lyman-alpha wavelength yields both CN(A)(v=0) and a range of rovibrationally excited CN(A) products but, in contrast to HCN, no significant branching to CN(B) products is observed. The corresponding beta parameter, which is found to be relatively invariant with CN internal energy, indicates a near limiting perpendicular distribution of D atom velocities about the photolysis radiation. These results are interpreted with reference to the available ab initio calculated potential energy surfaces of A' and A " symmetry, and the relative propensities for excitation to, and the likely dynamics on, these various excited states is discussed.