Polymers containing catechol groups have gained a large interest, as they mimic an essential feature of mussel adhesive proteins that allow strong binding to a large variety of surfaces under water. This feature has made this class of polymers interesting for surface modification purposes, as layer functionalities can be introduced by a simple adsorption process, where the catechol groups should provide a strong anchoring to the surface. In this work, we utilize an AFM-based method to evaluate the wear resistance of such polymer layers in water and compare it with that offered by electrostatically driven adsorption. We pay particular attention to two block copolymer systems where the anchoring group in one case is an uncharged catechol-containing block and in the other case a positively charged and catechol-containing block. The wear resistance is evaluated in terms of wear volume, and here, we compare with data for similar copolymers with statistical distribution of the catechol groups. Monitoring of nanomechanical properties provides an alternative way of illustrating the effect of wear, and we use modeling to show that the stiffness, as probed by an AFM tip, of the soft layer residing on a hard substrate increases as the thickness of the layer decreases. The stick-slip characteristics are also evaluated.