Electronic structure studies and quantum scattering methods are used to elucidate the differing reactivities of methane on Ni(111) and Pt(111). For both surfaces the lowest energy pathway to dissociation is over the top site, where the static surface barrier to reaction is about 0.14 eV lower on Pt(111) than on Ni(111). If allowed to relax, both surfaces exhibit a puckering of the metal atoms in the vicinity of the adsorbates and at the transition state. Thus, motion of the lattice can change the barrier to reaction. A quantum model for dissociation is employed that includes several molecular coordinates, and allows for coupling to the lattice motion and puckering of the lattice. We find that on Ni(111) the lattice has time to pucker, increasing the reactivity relative to the static surface case. The more massive atoms on the Pt(111) surface do not have time to pucker during the reaction. As both lattices become vibrationally excited the reactivity increases significantly, particularly at low incident energies where tunneling dominates. Our model suggests that tunneling is important for these large barrier systems, particularly at the relatively low incident energies of the experiments. Our work also suggests that at the large nozzle temperatures of the experiments, there are contributions to the total reactivity from vibrationally excited molecules, particularly for Ni(111). Our model is in reasonable agreement with the experimental results for Ni(111), while we significantly underestimate the reactivity on Pt(111) as well as the difference in reactivity between Ni(111) and Pt(111). This may result from errors in our total-energy calculations and/or effects due to motion (tunneling) of the methyl group at the transition state.