The performance of the CdTe radiation detectors heavily relies on the method of contact preparation. A convenient research method addressing this problem is the laser-induced transient current technique. In this paper, we compare the performance of two CdTe crystals which underwent different metallization processes. We showed that appropriately designed Au/Al contacts induce much less bulk polarization than commercial Pt/In electrodes under the same working conditions and can thus provide a convenient alternative to the industry standard. The comparison was based on the monitoring of the time-dependent sensor polarization measuring transient currents excited by above-bandgap laser illumination complemented by the Am 241 gamma spectroscopy. The theoretical analysis of current waveforms and radiation spectra enabled us to determine the charge carrier mobility, mobility-lifetime products of electrons and holes, and temporal and bias dependence of the space charge formation.