Lead‐based halide perovskite crystals are shown to have strongly anharmonic structural dynamics. This behavior is important because it may be the origin of their exceptional photovoltaic properties. The double perovskite, Cs2AgBiBr6, has been recently studied as a lead‐free alternative for optoelectronic applications. However, it does not exhibit the excellent photovoltaic activity of the lead‐based halide perovskites. Therefore, to explore the correlation between the anharmonic structural dynamics and optoelectronic properties in lead‐based halide perovskites, the structural dynamics of Cs2AgBiBr6 are investigated and are compared to its lead‐based analog, CsPbBr3. Using temperature‐dependent Raman measurements, it is found that both materials are indeed strongly anharmonic. Nonetheless, the expression of their anharmonic behavior is markedly different. Cs2AgBiBr6 has well‐defined normal modes throughout the measured temperature range, while CsPbBr3 exhibits a complete breakdown of the normal‐mode picture above 200 K. It is suggested that the breakdown of the normal‐mode picture implies that the average crystal structure may not be a proper starting point to understand the electronic properties of the crystal. In addition to our main findings, an unreported phase of Cs2AgBiBr6 is also discovered below ≈37 K.