Using the inelastic x-ray scattering (IXS) technique, we investigate the lattice dynamics of inorganic--organic hybrid iodide perovskites ${\mathrm{FAPbI}}_{3}$ and ${\mathrm{FASnI}}_{3}$ (FA $\ensuremath{\equiv}\phantom{\rule{4pt}{0ex}}\mathrm{CH}{({\mathrm{NH}}_{2})}_{2}$, formamidinium) in their cubic $\ensuremath{\alpha}$ phase and tetragonal $\ensuremath{\beta}$ phase. We find that the IXS spectra of ${\mathrm{FASnI}}_{3}$ are highly broad at all momentum points, as has been widely observed in the Pb-based halide perovskites. The speeds of sound (phonon group velocities) and absolute values of elastic constants of ${\mathrm{FASnI}}_{3}$ are smaller than those of ${\mathrm{FAPbI}}_{3}$ in both phases. In addition, no significant difference in the phonon lifetimes of ${\mathrm{FAPbI}}_{3}$ and ${\mathrm{FASnI}}_{3}$ is observed. These results correlate better with the reported tendency that the lattice thermal conductivity of ${\mathrm{ASnX}}_{3}$ is lower than that of ${\mathrm{APbX}}_{3}$. We discuss that our results also favor the up-conversion mechanism by acoustic phonons in the phonon bottleneck effect for the long lifetime of hot carriers.