We study the effect of the length scales alpha and beta in the Navier-Stokes- alphabeta equations on the energy spectrum and the alignment between the vorticity and the eigenvectors of the stretching tensor in three-dimensional homogeneous and isotropic turbulent flows in a periodic cubic domain, including the limiting cases of the Navier-Stokes- alpha and Navier-Stokes equations. A significant increase in the accuracy of the energy spectrum at large wave numbers arises for beta<alpha . The vorticity structures predicted by the Navier-Stokes- alphabeta equations also improve as beta decreases away from alpha . However, optimal choices for alpha and beta depend not only on the problem of interest but also on the grid resolution.