A comprehensive model comparison is presented for the description of the steady state and dynamic behavior of a wall-cooled fixed bed methanation reactor. First, the maximal conversion predicted by different steady state models is compared and evaluated. Second, the dynamic reactor behavior is investigated based on positive and negative step changes of the inlet flow rate. The examined model complexity ranges from a simple one-dimensional pseudohomogeneous reactor model to a two-dimensional heterogeneous model. The results show that similar maximal conversions are predicted by each model, but large discrepancies appear for the prediction of the dynamic reactor behavior. Our data clarify the impact of the considered heat and mass transfer resistances on the model prediction and allow us to give specific recommendations for further steady state and dynamic modeling works.