Reaction modelling of methane/hydrogen combustion has two important aspects. First, such mixtures may be used in future in combustion devices like gas turbines and gas engines in the frame of the demand for efficient energy storage systems, where the amount of hydrogen in natural gas delivering systems may vary according to varying hydrogen production from renewable energies. Second, this can be an important aspect for safety, as such mixtures may occur in disastrous situations and calculations may allow the prediction of safety issues. Modelling of such mixed fuel combustion processes is non-trivial due to the involved preferential diffusion effects, coming from the different diffusivities of methane and hydrogen. In turbulent flame modelling, this topic is of special interest, as also thermo-diffusive instabilities and local influence of the local burning velocity near leading edges of the flame seem to be of importance even for highly turbulent flames. This numerical work deals therefore with a comparative study of five different turbulent combustion models - Bray Moss-Libby, Linstedt-Vaos (LV), a modified version LV, Turbulent Flamespeed Closure, and Algebraic Flame Surface Wrinkling model - to the situation of turbulent methane/hydrogen/air flames. Validation is done with extensive experimental data obtained by a low swirl burner in the group by Cheng. Besides a basic case with pure methane/air, special emphasis is laid on flames with 40 to 100 % hydrogen content by volume. It is shown that for such methane/hydrogen fuel mixtures common reaction rate models are not sufficient where the fuel effects are included only via a laminar flame speed. Instead, a recently proposed reaction model with the incorporation of an effective Lewis number of the fuel mixture is found to work rather well. This is of both, practical as well as theoretical importance, as for the latter it confirms controversially discussed assumptions of the influence of preferential diffusion.