We discuss common features and differences in the fully differential cross sections (FDCS) for the electron-impact double ionization of He evaluated using the convergent close-coupling (CCC) method and various methods that utilize the three-body Coulomb wavefunctions (3C and C4FS). The calculations are restricted to the first Born approximation with respect to the interaction of the fast projectile with the target. In contrast to the similar (γ, 2e) reactions, where predictions of all the above theories qualitatively agree, there is a systematic difference between the FDCS calculated in the CCC and the 3C-type theories which is amplified as the momentum transfer from the projectile to the target increases. We argue that this fact is an indication that the P partial wave of a two-electron final state wavefunction is well described by the 3C model, but higher partial waves are poorly treated.