We propose a rigorous comparison of two widely known dynamic information flow mechanisms: Secure Multi-Execution (SME) and Multiple Facets (MF). Informally, it is believed that MF simulates SME while providing better performance. Formally, it is well known that SME has stronger soundness guarantees than MF. Surprisingly, we discover that even if we approach them to enforce the same soundness guarantees, they are still different. While modeling them in the same language, we are able to precisely identify the features of the semantics that lead to their differences. In the process of comparing them, we also discovered four new mechanisms that share features of MF and SME. We prove that one of them simulates SME, which was falsely believed to be true for MF.