The deep-level defects in the Cd1-xZnxTe (CZT) and Cd1-xMnxTe (CMT) detectors are characterized by photo-induced current transient spectroscopy (PICTS), thermoelectric emission spectroscopy (TEES) and thermally stimulated current (TSC) measurements. Two different types of CZT crystals are considered for trap characterization; the first type is grown by using vertical Bridgman (VB) method and treated with oxygen plasma for surface passivation, whereas the second type is grown by the VB arrangement with accelerated crucible rotation technique (ACRT). The CMT samples used in defect characterization studies are grown by the VB method. The deep-level donor responsible for the electrical compensation in the CZT and CMT bulk is identified from the steady-state thermal generation current characteristics. From the PICTS and TEES results, the trap signatures in the various CZT and CMT detectors are analyzed and compared in terms of their energy level, capture cross-section, and carrier detrapping time of the defects. Furthermore, DC photoconductivity measurements are conducted to assess the carrier mobility-lifetime (µτ) product in the CZT and CMT crystals. The midgap states at 0.81-0.85 eV are found in all the CZT and CMT crystals and these deep-level traps should play a significant role in carrier compensation along with the deep-level donors (EDD = 0.78-0.84 eV). To the best of our knowledge, three new traps at EV + 0.22 eV, EC-0.68 eV and EC-0.7 eV are identified in the CMT crystals for the first time in the literature. The reported deep-level defects are intended to provide excellent feedback to the CZT and CMT bulk growth community for the radiation detector technology developments.