Two different kinetic theories [J. Solsvik and E. Manger (SM-theory), Phys. Fluids \textbf{33}, 043321 (2021) V. Garz\'o, J. W. Dufty, C. M. Hrenya (GDH-theory), Rev. E \textbf{76}, 031303 (2007)] are considered to determine the shear viscosity $\eta$ for a moderately dense granular binary mixture of smooth hard spheres. The is subjected simple flow heated by action an external driving force (G...