Using a well-validated computational fluid dynamics simulation method, based on a multi-ion transport model, a detailed analysis of the differences in band broadening between pressure-driven (PD) and electrically driven (ED) flows through perfectly ordered, identical chromatographic pillar packings has been made. It was found that, although the eddy-diffusion band-broadening contributions were nearly completely absent in the considered structure, the ED flow still yields much smaller plate heights than the PD flow. This difference could be fully attributed to the different ways in which the ED and PD velocity profiles reshape when passing through a tortuous pore structure with undulating cross section. Whereas in the PD case the parabolic tip of the band front is continually squeezed and extended each time it passes a pore constriction, the ED flow displays some kind of band front restoring mechanism, with which the fluid elements of the band front are (at least partly) laterally re-aligned after each pore constriction passage. This could be clearly visualized from a series of step-by-step images of the progression of a sharply "injected" species band moving through the packing under ED and PD conditions.