Adsorption profiles and conformational properties of negatively charged polyions at responsive surfaces were investigated by Monte Carlo simulations using a simple coarse-grained model. The surface, carrying both negative and positively charged groups, presents different overall charge, ranging from -10 to +50 e, and states, where the surface groups are either in a liquid-like structure (frozen surface) or laterally mobile (fluid surface). Polyions with both linear and ring architectures are considered. We have found that for very attractive surfaces the classical picture of a strongly adsorbed polyion with an extended and flat conformation emerges, independently of the architecture of the polyion or the state of the surface. At weakly attractive surfaces, the ring polyion adsorbs more strongly since it loses less entropy on adsorption than a linear chain. The adsorption of the ring is also enhanced at the fluid surfaces, since its more compact conformation increases the polarization of the surface. However, the linear polyion shows a significant adsorption at a neutral fluid surface, while the ring chains are totally desorbed, suggesting a delicate balance between the entropy of the surface groups and that of the chains. Although ring polyions show a stronger adsorption and a more compact conformation both in- and out-of-plane, at weakly attractive surfaces, no significant influence of the architecture was found on the polyion induced surface polarization (fluid surfaces) or opposite charge patch detection (frozen surfaces), at the monomer level. The adsorption profiles are, however, very different. For linear polyions at weakly attractive surfaces, it was observed a strong predominance of one-tail conformations, which was independent of the state of the surface.