Based on two versions of Maxwell’s Equations we investigate the Poynting vector, the energy transport and the dispersion relation both for right- and left-handed systems. Furthermore, it is shown that the latter systems are necessarily dispersive in contrast to the former ones. In the end we discuss a published example where the mixing of expressions of both versions of Maxwell’s Equations leads to unphysical conclusions. The presentation demonstrates for students how flexible can be the work with different versions of electrodynamics but also how carefully one has to be thereby.