We report melting points and other thermal properties of several semiconducting and metallic elements as they are modeled by different empirical interatomic potential models, including the Stillinger-Weber, the embedded-atom method, the Finnis-Sinclair and the modified-embedded-atom method. The state-of-the-art free energy methods are used to determine the melting points of these models within a very small error bar, so that they can be cross-compared with each other. The comparison reveals several systematic trends among elements with the same crystal structure. It identifies areas that require caution in the application of these models and suggests directions for their future improvement.