Bimetallic nanoparticles often turn out to be superior to the corresponding monometallic systems with respect to their catalytic properties. To study such effects for the methanol decomposition reaction, model catalysts were prepared by physical vapor deposition of Pd and Co under ultrahigh-vacuum (UHV) conditions. Monometallic Pd and Co particles as well as CoPd core-shell particles were generated on an epitaxial alumina film grown on NiAl(110). The interaction with methanol is examined by temperature-programmed desorption of methanol and carbon monoxide and by X-ray photoelectron spectroscopy. The decomposition of methanol proceeds in two reaction pathways independent of the particle composition: complete dehydrogenation towards carbon monoxide and hydrogen, and C--O bond scission yielding carbon deposits. Pd is the most active material studied here. The relative importance of the two channels varies for the different particle systems: on Pd dehydrogenation is preferred, whereas the C--O bond cleavage is more pronounced on Co. The bimetallic clusters show a moderate performance for both pathways. Carbon deposition poisons the model catalysts by blocking the adsorption sites for methoxide, which is the first intermediate product during methanol decomposition. In particular on Co, large amounts of carbon deposits can also be caused by dissociation of the final product of the dehydrogenation pathway, carbon monoxide. A comparison with the results of methanol decomposition on Co, Pd, and CoPd catalysts in continuous-flow reactors demonstrates that the findings of the present UHV study are relevant for catalytic performance under high-pressure conditions.