Missense variants that alter a single amino acid in the encoded protein contribute to many human disorders but pose a substantial challenge in interpretation. Though these variants can be reliably identified through sequencing, distinguishing the clinically significant ones remains difficult, such that "Variants of Unknown Significance" outnumber those classified as "Pathogenic" or "Likely Pathogenic." Numerous in silico approaches have been developed to predict the functional impact of missense variants to inform clinical interpretation, the latest being AlphaMissense, which uses artificial intelligence methods trained on predicted protein structure. To independently assess the performance of AlphaMissense and 38 other predictors of missense severity, we compared predictions to data from multiplexed assays of variant effect (MAVE). MAVE experiments generate almost every possible individual amino acid change in a gene and measure their functional impact using a high-throughput assay. Assessing 17,696 variants across five genes (DDX3X, MSH2, PTEN, KCNQ4, and BRCA1), we find that AlphaMissense is consistently one of the top five algorithms based on correlation with functional impact and is the best-correlated algorithm for two genes. We conclude that AlphaMissense represents the current best-in-class predictor by this metric; however, the improvement over other algorithms is modest. We note that multiple missense predictors, including AlphaMissense, appear to overcall variants as pathogenic despite minimal functional impact and that substantially more high-quality training data, including consistently analyzed patient cohorts and MAVE analyses, are required to improve accuracy.