Recent advances in 3D graphics technologies have led to an increasing use of processing techniques on 3D meshes, such as filtering, compression, watermarking, simplification, deformation and so forth. Since these processes may modify the visual appearance of the 3D objects, several metrics have been introduced so as to properly drive or evaluate them, from classic geometric ones such as Hausdorff distance, to more complex perceptually-based measures. This paper presents a survey on existing perceptually-based metrics for visual impairment of 3D objects and provides an extensive comparison between them. In particular, different scenarios which correspond to different perceptual and cognitive mechanisms are analyzed. The objective is twofold: (1) catching the behavior of existing measures so as to help Perception researchers for designing new 3D metrics and (2) providing a comparison between them so as to inform and help Computer Graphics researchers for choosing the accurate tool for the design and the evaluation of their mesh processing algorithms.