The interaction of Pd with the Al-terminated alpha-Al2O3(0001) surface has been investigated using an embedded cluster model and periodic-supercell approaches. Furthermore. several treatments of electronic exchange and correlation within density functional (DF) theory have been employed including generalized gradient approximation (GGA) and hybrid exchange functionals. In the periodic calculations the influence of pseudopotentials and basis sets have also been investigated by comparing GGA results obtained using all electron basis set and pseudopotential plane-wave approaches. For a given choice of the exchange-correlation functional and for a fixed substrate, the cluster and stab models predict nearly the same structural parameters and adsorption energies. All structural models reproduce the general trend for the interaction of Pd with the alpha-Al2O3(0001) surface. which is that there is a slight preference for adsorption above surface sites sitting directly above oxygen atoms either from the second or fifth layer. However, significantly larger differences exist when comparing different DF methods within a given surface model. The cluster and periodic slab models predict a large adsorbate-induced relaxation with a similar description of the metal-oxide interface provided a minimum number of surface layers is included in the optimization procedure.