This paper studies the thermodynamic properties of the competitive adsorption between two polymer species differing only in length onto a flat wall from dilute solution by both mean-field and scaling theories. The employed mean-field approach is based on a recently developed theory for monodisperse solutions, which goes beyond the usual ground-state approximation to account for the contribution of the tails. As in the monodisperse case we also find a crossover length z* which separates a loop-dominated region adjacent to the wall from a tail-dominated region farther away from the wall. This length scale strongly depends on the length of both chains and is the relevant scaling variable for the loop and tail concentration profiles. The space variation of these profiles and the adsorbances are discussed in detail. We find a strong adsorption preference for the long chains, which is very pronounced in dilute solution. This result parallels those of experiments and, in its mean-field version, can be compared quantitatively with the numerical calculations of the Scheutjens-Fleer theory [G. J. Fleer et al., Polymers at Interfaces (Chapman and Hall, London, 1993)]. However, mean-field theory predicts that the adsorbances depend only on the ratio of the two chain lengths, whereas an absolute dependence on chain length is found by scaling theory. Since the scaling theory extends the mean-field treatment to good solvent conditions, this qualitative difference between both theoretical approaches should be observable in experiments.