We give a comparison of various differential cross-section models for a classical polyatomic gas for a homogeneous relaxation problem and the shock wave profiles at Mach numbers 1.71 and 12.9. Besides the standard Borgnakke-Larsen model and its generalization to an energy dependent coefficient to control the amount of rotationally elastic and completely inelastic collision, we discuss some new models recently proposed by the same authors. Moreover, we present numerical algorithms to implement the models in a particle or Monte-Carlo code and compare the numerical shock wave profiles with existing experimental data.