Hydrogen bond symmetrization is a fundamental pressure-induced transformation in which the distinction between donor and acceptor sites vanishes, resulting in a symmetric hydrogen-bond network. While extensively studied in pure ice—most notably during the ice VII to ice X transition—this phenomenon remains less well characterized in hydrogen hydrates. In this work, we investigate hydrogen bond symmetrization in the high-pressure phases of hydrogen hydrates (H2-H2OandD2-D2O) through a combined approach of Raman spectroscopy and first-principles quantum atomistic simulations. We focus on the C2 and C3 filled-ice phases, using both hydrogenated and deuterated water frameworks. Our results reveal that quantum fluctuations and the interaction between the encaged H2 molecules and the host lattice play a crucial role in driving the symmetrization process. Remarkably, we find that in both C2 and C3 phases hydrogen bond symmetrization occurs via a continuous crossover at significantly lower pressures than in pure ice, without any change in the overall crystal symmetry. These findings provide insight into the quantum-driven mechanisms of bond symmetrization in complex hydrogen-bonded systems under extreme conditions.