The role of anisotropic scattering in rotational collisions of electrons with CO molecules is investigated numerically with Monte Carlo (MC) simulations and with calculations using the Lisbon KInetics two-term Boltzmann solver (LoKI- B). The study adopts integral cross sections taken from the IST-Lisbon database of LXCat or extracted from Biagi’s code Magboltz v11.10. Different angular scattering models for rotational collisions are implemented and compared in MC simulations, and a novel anisotropic scattering model is derived from the dipole-Born differential cross sections, to describe the strongly forward-peaked nature of rotational collisions. This model is also implemented in LoKI-B, to describe the anisotropic inelastic/superelastic scattering in dipole rotational collisions, using coherent expressions for the corresponding integral and momentum transfer cross sections. The comparison between MC and LoKI-B results shows that the calculation of swarm parameters is more influenced by the choice of the angular scattering model than the adoption of the two-term approximation, yielding deviations up to 50% in the reduced mobility for different angular distributions. The consequences in the swarm derivation of cross sections are also discussed. Finally, it is shown that inclusion of electric-quadrupole interactions, usually neglected in electron swarm studies, can improve the agreement between numerical results and measurements.