The self-consistent-field model for polymer adsorption of Scheutjens and Fleer is extended to the case of semiflexible chains in a cubic lattice. It is found that the scaling behavior for adsorption from a dilute solution of polymers with the same radius of gyration, but with a varying degree of stiffness, is markedly different. Adsorption from a semidilute solution gives a chain-length-independent profile, even when bond correlations are taken into account. Adsorbing block copolymers with blocks that differ only in the rigidity of the blocks adsorb with the stiffer block on the surface. This preference has an entropical origin. Such copolymers behave similar to "energetic" block copolymers, where the blocks differ in energetic interaction with the solvent or with the surface. The effects of chain stiffness are of the same order of magnitude as energetic effects.