We performed a comparative study of the adsorption of an in vitro selected peptide on two different carbon surfaces: a flat graphene and a curved (0,15) nanotube. The sequence was selected from recent experiments, as the one giving the highest carbon affinity for carbon nanotubes. Rigid docking of the molecule on the two surfaces by a genetic algorithm was followed by molecular dynamics simulations with empirical force fields (OPLS-AA) in water at finite temperature. The total free energies of folding and adhesion and the quality of surface binding were determined, based on a combination of solvation energy, formation of hydrogen bonds, and amount of the apolar (hydrophobic) contact surface between peptide and carbon surface. For both cases, we find a strong adhesion energy and large nonpolar contact surface. Isoleucines and tryptophans are the most strongly bound residues to the two carbon surfaces, the latter one largely dominating. In the case of the carbon nanotube, the peptide shows several competing stable structures, corresponding to different possible molecular foldings, and a propensity to enhance the intramolecular stability by forming new hydrogen bonds. In both systems, different arrangements of the histidine and tryptophan residues enable a better adaptation to the carbon surfaces. These findings suggest that the experimentally observed surface specificity of the peptide on nanotubes may depend on its capability to support multiple strongly bound configurations.