We studied the core-resonant double photoemission process from palladium films with linearly polarized synchrotron radiation. We excited either the 3d or 4p core level and focused on the Auger transitions which leave two holes in the valence band. We find that the two-dimensional energy distributions are markedly different for the 3d and 4p decay. The 3d decay can be understood by a sequential emission of the two electrons while the 4p decay proceeds in a single step. Despite the large differences in the two-dimensional energy spectra we find the shape of the energy sum spectra rather similar. For the description of the 4p decay we propose a model which uses available single electron spectra, but suggest an alternative interpretation of these data. With this we are able to explain the range over which the available energy is shared. Key assumptions of the model are verified by our experiments on the 3d decay.