[khuey]

Enthalpy of combustion for CH4 is 802 kJ and for an equivalent amount of gaseous hydrogen it's 286 kJ so most of the energy does come from the carbon.

[jjk166]

That's not how chemistry works. Burning 1 CH4 is not the same as burning 1 C and 2 H2. The formation of carbon dioxide (aka the combustion of carbon) contributes 393.5 kJ per mole of CH4 combusted, and the formation of water (aka the combustion of hydrogen) contributes 483.6 kJ per mole of CH4, the activation energy to split the CH4 molecule is 74.8 kJ per mole of CH4 combusted. So 55% of the heat released per mole is from the hydrogen.