Aiming to assess the quality of CTMQC dynamics for photon-electron-nuclear problems, we have studied two model situations illustrating nonadiabatic dynamics and spontaneous emission of an electron-nuclear system strongly coupled to a single-mode cavity in resonance with a typical electronic excitation window of the system. Our analysis of the exact factorization formalism was based on the analysis of the time-dependent potentials of the theory combined with the assessment of the performance of CTMQC. In particular, we employed the results of numerically-exact quantum-dynamics simulations as benchmark for CTMQC and we compared CT-MQC with multi-trajectory Ehrenfest and with Tully surface hopping. The calculations revealed that CTMQC and Ehrenfest presented better agreement with exact quantum dynamics than surface hopping in terms of average photon numbers and electronic populations all along the dynamics. How-ever, quantitative agreement with the reference results is lacking across all methods, but we pointed out the most probable source of error in CTMQC, which will be investigated further in the future. Specifically, the geometric component the timedependent potential energy surface, which is neglected in CT-MQC, showed to be dominant along the photonic coordinate for the considered systems, as it seems to have significant effect in the splitting of the photon density.