The complexity of a polygonal mesh model is usually reduced by applying a simplification method, resulting in a similar mesh having less vertices and faces. Although several such methods have been developed, only a few observer studies are reported comparing them regarding the perceived quality of the obtained simplified meshes, and it is not yet clear how the choice of a given method, and the level of simplification achieved, influence the quality of the resulting model, as perceived by the final users. Mesh quality indices are the obvious less costly alternative to user studies, but it is also not clear how they relate to perceived quality, and which indices best describe the users behavior. Following on earlier work carried out by the authors, but only for mesh models of the lungs, a comparison among the results of three simplification methods was performed through (1) quality indices and (2) a controlled experiment involving 65 observers, for a set of five reference mesh models of different kinds. These were simplified using two methods provided by the OpenMesh library - one using error quadrics, the other additionally using a normal flipping criterion - and also by the widely used QSlim method, for two simplification levels: 50% and 20% of the original number of faces. The main goal was to ascertain whether the findings previously obtained for lung models, through quality indices and a study with 32 observers, could be generalized to other types of models and confirmed for a larger number of observers. Data obtained using the quality indices and the results of the controlled experiment were compared and do confirm that some quality indices (e.g., geometric distance and normal deviation, as well as a new proposed weighted index) can be used, in specific circumstances, as reasonable estimators of the user perceived quality of mesh models.