Using Monte Carlo computer simulations, we contrast the surface adsorption of comb and linear polymers that contain the same number of monomers. Both homopolymers and copolymer chains are examined. The homopolymers are composed of units that are strongly attracted to the surface ("stickers"), while the copolymers contain both stickers and sites that do not have a high affinity for the surface. Comb polymers, which contain long "sticky" teeth, provide a higher or comparable surface coverage, thinner films, and greater polymer-surface adhesion and wettability than the equivalent linear chains. For homopolymer and copolymer combs that contain sticky teeth, the behavior of the long teeth dominate the properties of the chains at the interface. Thus differences between these two types of chains diminish as the tooth length is increased. Finally, combs that contain sticky backbones but nonsticky teeth provide a significant polymer density in the outer layers of the adsorbed film. Thus the width of the adlayer can be tailored by varying the location of the stickers in the comb polymers.