We report on comparison between temperature-dependent magneto¬absorption and magnetotransport spectroscopy of HgTe/CdHgTe quantum wells in terms of detection of phase transition between topological insulator and band insulator states. Our results demonstrate that temperature-dependent magnetospectroscopy is a powerful tool to discriminate trivial and topological insulator phases, yet magnetotransport method is shown to have advantages for clear manifestation of the phase transition with accurate quantitative values of transition parameter (i.e. critical magnetic field Bc).