The interaction of (two-level) Rydberg atoms with dissipative QED cavity fields can be described classically or quantum mechanically, even for very low temperatures and mean number of photons, provided the damping constant is large enough. We investigate the quantum-classical border, the entanglement and decoherence of an analytically solvable model, analog to the atom-cavity system, in which the atom (field) is represented by a (driven and damped) harmonic oscillator. The maximum value of entanglement is shown to depend on the initial state and the dissipation-rate to coupling-constant ratio. While in the original model the atomic entropy never grows appreciably (for large dissipation rates), in our model it reaches a maximum before decreasing. Although both models predict small values of entanglement and dissipation, for fixed times of the order of the inverse of the coupling constant and large dissipation rates, these quantities decrease faster, as a function of the ratio of the dissipation rate to the coupling constant, in our model.