For general symmetric multi-qubit systems, the behavior of oneand two-qubit entanglement for Dicke, spin coherent and parity-adapted (even and odd) spin coherent states is determined. These quantum correlations are quantified by linear and von Neumann entropies of the corresponding one-and two-qubit reduced density matrices of the multi-qubit system. These states play a fundamental role in the study of Hamiltonian systems written in terms of collective generators of the angular momentum algebra like, for example, the Lipkin-Meshkov-Glick (LMG) model. Here we shall use these entanglement measures as a signature to characterize the dierent quantum phases that appear in these models.