  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-classical
versions of the models. The presence of chaos for different energies and
coupling constants is exhibited, employing Poincar\'e sections and Peres
lattices in the classical and quantum versions, respectively. A clear
correspondence between the classical and quantum result is found for systems
containing between $\mathcal{N} = 80$ to $200$ atoms. A measure of the Wigner
character of the energy spectrum for different couplings and energy intervals
is also presented employing the statistical Anderson-Darling test. It is found
that in the Dicke Model, for any coupling, a low energy regime with regular
states is always present. The richness of the onset of chaos is discussed both
for finite quantum systems and for the semi-classical limit, which is exact
when the number of atoms in the system tends to infinite.
