The non-integrable Dicke model and its integrable approximation, the Tavis-Cummings (TC) model, are studied as functions of both the coupling constant and the excitation energy. The present contribution extends the analysis presented in the previous
paper by focusing on the statistical properties of the quantum fluctuations in the energy spectrum and their relation with the excited state quantum phase transitions (ESQPT). These properties are compared with the dynamics observed in the semi-classica
