The main macroscopic difference between the two models is that the only IGRF representation of the geomagnetic field is essentially symmetric, while the magnetosphere is highly asymmetric. We found the day-night asymmetry in the calculated total magnetic field values only using also the external field, perfectly corresponding to the day-night sides (see the following figure, specially when the distance from the center of the Earth is 10 Earth radii).
Figure 1: Comparison between only internal magnetic field strenght (right) and internal plus external magnetic field (left) at different Earth radii in geographic coordinates. The bottom figure represents the day and night side, corresponding to the time of the simulation (source: http://www.fourmilab.ch/cgi-bin/uncgi/Earth/action?opt=-p 2014).