  A quantitative comparison between the results of shear viscosities from the
Chapman-Enskog and relaxation time methods is performed for selected test cases
with specified elastic differential cross sections: (i) the non-relativistic,
relativistic and ultra-relativistic hard sphere gas with angle and energy
independent differential cross section, (ii) the Maxwell gas, (iii) chiral
pions and (iv) massive pions. Our quantitative results reveal that the extent
of agreement (or disagreement) depends very sensitively on the energy
dependence of the differential cross sections employed.
