Direct numerical simulations of three-dimensional compressible magnetohydrodynamic (MHD) turbulence have been performed in order to study the relation between wave modes and coherent structures and the consequent energization of test particles. Moreover, the question of which is the main mechanism of this particle energization is rigorously discussed. In particular, using the same initial conditions, we analyzed the nonlinear and linear evolution of a turbulent state along with the case of randomized phases. Then, the behaviors of the linear and nonlinear simulations were compared through the study of the time evolution of particle kinetic energy and preferential concentration. Also, spatiotemporal spectra were used to identify the presence of wave modes and quantify the fraction of energy around the MHD modes in linear and nonlinear simulations. Finally, the variation of the correlation time of the external forcing is studied in detail along with the effect on the particle energization (and clustering) and the presence of wave modes. More specifically, particle energization tends to decrease when the fraction of linear energy increases, supporting the idea that energization by structures is the dominant mechanism for particle energization instead of resonance with wave modes as suggested by Fermi energization theory.