  We investigate spin squeezing, quantum entanglement and second order
coherence in two coupled, driven, dissipative, nonlinear cavities. We compare
these quantum statistical properties for the cavities coupled with either
single or two-photon exchange. Solving the quantum optical master equation of
the system numerically in the steady state, we calculate the zero-time delay
second-order correlation function for the coherence, genuine two-mode
entanglement parameter, and an optimal spin squeezing inequality associated
with particle entanglement. We identify regimes of distinct quantum statistical
character depending on the relative strength of photon-exchange and
nonlinearity. Moreover, we examine the effects of weak and strong drives on
these quantum statistical regimes.
