  We compare the entire classical and quantum evolutions of the Dicke model in
its regular and chaotic domains. This is a paradigmatic interacting spin-boson
model of great experimental interest. By studying the classical and quantum
survival probabilities of initial coherent states, we identify features of the
long-time dynamics that are purely quantum and discuss their impact on the
equilibration times. We show that the ratio between the quantum and classical
asymptotic values of the survival probability serves as a metric to determine
the proximity to a separatrix in the regular regime and to distinguish between
two manifestations of quantum chaos: scarring and ergodicity. In the case of
maximal quantum ergodicity, our results are analytical and show that quantum
equilibration takes longer than classical equilibration.
