Why carbon monoxide reacts with hydrogen to give different products in the presence of different catalysts
The thermodynamics are always the same. If you go from carbon monoxide to methane, there is only one final enthalpy, and if you have the choice of going to methane or methanol the thermodynamically preferred product is always the same.

The difference indeed less within the different pathways and the activation barriers needed to get from one intermediate to the next. This isn’t really thermodynamics, it is mainly kinetics (although you can argue about thermodynamically preferred intermediates). The pathways are often very complex and entire papers revolve around how one reaction is catalysed on such a solid state catalyst, so please forgive me for not looking them up; but the general point still stands: one catalyst will lead to intermediates where the $\ce{C-O}$ bond is easily broken (and thus give methane), the other will not (and thus give methanol).