An abundant source of CH4 can be found in natural hydrate deposits. Recent demonstration of CH4 recovery from hydrates via CO2 exchange has revealed the potential as a fuel source that also provides a medium for carbon sequestration. It is vital to understand the structural and dynamic impacts of guest variation in CH4, CO2, and mixed hydrates and link the results to the stability of various deposits in nature, harvesting methane, and sequestering CO2. Molecular vibrations are examined in CH4, CO2, and mixed CH4-CO2 hydrates at 5 and 190 K and Xe hydrates for comparison. Inelastic neutron scattering (INS) is an ideal spectroscopy technique to observe the dynamic modes in the hydrate structure and enclathrated CH4, as it is extremely sensitive to 1H. The presence of CO2 in hydrates tightens the lattice. It introduces more active librational modes to the host lattice, while hindering the motion of CH4 in mixed CH4-CO2 hydrate at 5 K. At 190 K, a large broadening of the CH4 librational modes indicates disorder in the structure leading to dissociation.