Identification of a structural damage becomes critically important step of proper maintenance of structural elements being in operation according to the widely accepted damage tolerance philosophy in numerous industrial branches related to the construction engineering. Within the variety of available testing methods, vibration-based methods, due to their effectiveness and low cost, are used in such inspection. However, to detect small or early damage in structures, additional processing of the measurement results is necessary. In this paper, two principally different approaches of damage identification in composite plates based on the damage indices and the curvelet transform were analyzed and compared in the light of evaluation of sensitivity to damage, robustness to measurement and processing noise, and accuracy of estimation of a damage. The obtained results of this comparative study clearly indicate the superiority of the curvelet transform, which allowed not only properly identify damage thanks to the enhanced directional selectivity, but simultaneously reduce measurement noise, which makes it an excellent candidate for effective identification of damage in various engineering structures.