In this paper we study in detail the influence of the longitudinal constant electric field on the energy values of a digital quantum well AlxGa1-xAs/GaAs structure and its equivalent graded-composition analog quantum well. We calculate the energies of the electron and hole bound states, the energies of the main optical transitions and their Stark shifts. The spatial distributions of the main electronic and hole states at various given values of the applied electric field are also calculated. The semi-empirical tight-binding approximation in the spin dependent sp3s* basis is used and is carried out by surface Green function matching employing an algorithm previously developed and used to study inhomogeneous systems. The aim of these calculations is to find out in detail to what extent these two structures have similar or different properties in the presence of an applied electric field. We compare our results with the results for the conventional rectangular quantum well and with the available experimental data for quantum wells with similar parameters.