Molecular dynamics simulations of methane hydrate have been carried out using the polarizable AMOEBA and COS/G2 force fields. Properties calculated include the temperature dependence of the lattice constant, the OC and OO radial distribution functions, and the vibrational spectra. Both the AMOEBA and COS/G2 force fields are found to successfully account for the available experimental data, with overall somewhat better agreement with experiment being found for the AMOEBA model. Comparison is made with previous results obtained using TIP4P and SPC/E effective two-body force fields and the polarizable TIP4P-FQ force field, which allows for in-plane polarization only. Significant differences are found between the properties calculated using the TIP4P-FQ model and those obtained using the other models, indicating an inadequacy of restricting explicit polarization to in-plane only.