A comparison between two multimoment approaches is provided in the context of an application to the terrestrial polar wind. We compare the bi-Maxwellian 16-moment approach with the 16-moment generalized model, which has been built in order to account for the suprathermal part of the velocity distribution function better than the previous multimoment approaches. This comparison has shown a general similarity between the two approaches and has shown that the better adapted closure assumption of the set of transport equations of the generalized model generates a higher acceleration. Moreover, the better determination of the collisional energy transfers generates a smaller increase of the temperature of the supersonic species that generally agrees with the adiabatic cooling assumption predicted by Monte Carlo or direct resolution of the Fokker Planck equation. The generalized model also provides the typical profiles of the velocity distribution function from the original collision-dominated region to the collisionless region. These profiles are in good agreement with the Monte Carlo and collision kinetic resolution in the collision-dominated region and in the lower part of the transition region. ¿ 2000 American Geophysical Union