In this study, a detailed comparison of magneto-optical (MO) properties of HgS, GaSb, and GaAs Poschl- Teller quantum wells (PTQWs) is studied based on the optically detected magneto-phonon resonance (ODMPR) effect. Utilizing the operator projection method and profile technique, the MO-absorption power (AP) in the PTQWs and the full width at half maximum (FWHM) of the ODMPR-peaks due to the LO-phonons absorption and emission are calculated respectively. The results of the research show that the FWHM of the LO-phonon emission ODMPR-peak in the PTQW is always smaller than that of the LO-phonon absorption ODMPR-peak for both the three GaAs, HgS, and GaSb materials. In particular, the results also demonstrate that for the PTQW model, the MO-properties of the HgS material are remarkably different from those of the GaAs and GaSb materials, namely: (i) The FWHM of the LO-phonon emission ODMPR-peak in the PTQW is always smaller than that of the LO-phonon absorption ODMPR-peak. (ii) For the variation of the FWHM with the width of the PTQW, the concentration of the electron, and the temperature of the electron system: in the LO-phonon absorption ODMPR-peak case, the FWHM of the GaAs material is the largest, while that of the GaSb material is the smallest among the three GaAs, HgS, and GaSb materials; whereas, in the LO-phonon emission ODMPR-peak case, the FWHM of the HgS material is the largest, while that of the GaSb material is the smallest among the three GaAs, HgS, and GaSb materials. (iii) For the variation of the FWHM with the magnetic field: the FWHM of both the LO-phonons absorption and emission ODMPR-peaks in the PTQW of the HgS material is always the largest, while that of the GaSb material is always the smallest among the three GaAs, HgS, and GaSb materials.