Bidirectional Reflectance Distribution Functions (BRDFs) are pivotal to the perceived realism in image synthesis. While measured BRDF datasets are available, reflectance functions are most of the time approximated by analytical formulas for storage efficiency reasons. These approximations are often obtained by minimizing metrics such as $L_2$---or weighted quadratic---distances, but these metrics do not usually correlate well with perceptual quality when the BRDF is used in a rendering context, which motivates a perceptual study. The contributions of this paper are threefold. First, we perform a large-scale user study to assess the perceptual quality of 2026 BRDF approximations, resulting in 84138 judgments across 1005 unique participants. We explore this dataset and analyze perceptual scores based on material type and illumination. Second, we assess nine analytical BRDF models in their ability to approximate tabulated BRDFs. Third, we assess several image-based and BRDF-based ($L_p$, optimal transport and kernel distance) metrics in their ability to approximate perceptual similarity judgments.