The photodissociation dynamics of HI and DI are examined using time-dependent wave-packet techniques. The orientation and alignment parameters a_Q^(K)(p) are determined as a function of photolysis energy for the resulting ground-state I(²P_3/2) and excited-state I(²P_1/2) atoms. The a_Q^(K)(p) parameters describe the coherent and incoherent contributions to the angular momentum distributions from the A ¹Π₁, a ³Π₁, and t ³Σ₁ electronic states accessed by perpendicular excitation and the a ³Π₀₊ state accessed by a parallel transition. The outcomes of the dynamics based on both shifted ab initio results and three empirical models for the potential-energy curves and transition dipole moments are compared and contrasted. It is demonstrated that experimental measurement of the a_Q^(K)(p) parameters for the excitation from the vibrational ground state (v=0) would be able to distinguish between the available models for the HI potential-energy curves and transition dipole moments. The differences between the a_Q^(K)(p) parameters for the excitation from v=0 stand in sharp contrast to the scalar properties, i.e., total cross section and I* branching fraction, which require experimental measurement of photodissociation from excited vibrational states (v > 0) to distinguish between the models.