The Vicsek model describes the motion of aligning active particles, but the hydrodynamic theory is not fully resolved. This paper investigates a unified moment-closure framework for three Vicsek-type kinetic equations, covering Fokker-Planck models of Degond-Vicsek and Degond-Frouvelle-Liu type, as well as Bertin’s Boltzmann formulation. Using a simple P_N closure, where higher-order Fourier moments are truncated, we systematically derive finite-dimensional moment systems from the underlying kinetic equations. Within this unified setting, we analyse the collision operators and characterize the sets of spatially homogeneous equilibria, i.e. moment states where the collision terms vanish. The structure of equilibria and their dependence on noise and model parameters are explicitly identified for low-order closures. We further study the linear stability of homogeneous equilibria under spatial perturbations and derive necessary stability conditions at the hydrodynamic level. The analysis is further supported by numerical tests. This work provides a transparent comparison of Vicsek-type models through a common moment-based description.