Three palladium catalysts at similar loadings supported on few-layers graphene (FLG), carbon nanotubes (CNT) and carbon nanofibers (CNF) have been prepared by wet impregnation of palladium nitrate with the purpose of determine the influence of the support on Pd catalytic activity. The supports and catalysts have been characterized by chemical analysis, Raman spectroscopy, XRD, electron microscopy and XPS. The average Pd particle size depends on the carbon support, ranging from 1.6 nm for CNF to 2.6 nm for FLG. The catalytic activity of these catalysts was evaluated for two different reactions of interest for biomass transformations, namely hydrodeoxygenation of vanillin to 2-methoxy-4-methyl-phenol (creosol) that requires a bifunctional catalyst with hydrogenating and Lewis acid sites, and aerobic oxidation of 5-hydroxymethylfurfural to 2,5-furandicarboxylic acid. Both compounds have application either as food flavouring additive and polyester co-monomer. For the two reactions the activity order of the fresh catalyst was Pd/FLG > Pd/CNF > Pd/CNT, indicating that FLG contributes favorably to the activity in spite of the larger Pd size of the nanoparticles on this support, a fact that has been attributed to the interaction with the prismatic planes on where Pd nanoparticles are located.