We investigated the correlation between the polymer backbone structural regularity and the charge transport properties of poly{N,N′-bis(2-octyldodecyl)-1,4,5,8-naphthalenediimide-2,6-diyl-alt-5,5′-(2,2′-bithiophene)} P(NDI2OD-T2), a widely studied semiconducting polymer exhibiting high electron mobility and an unconventional micromorphology. To understand the influence of the chemical structure and crystal packing of conventional regioregular P(NDI2OD-T2) RR-P(NDI2OD-T2) on the charge transport, the corresponding regioirregular polymer RI-P(NDI2OD-T2) was synthesized. By combining optical, X-ray, and transmission electron microscopy data, we quantitatively characterized the aggregation, crystallization, and backbone orientation of all of the polymer films, which were then correlated to the electron mobilities in electron-only diodes. By carefully selecting the preparation conditions, we were able to obtain RR-P(NDI2OD-T2) films with similar crystalline structure along the three crystallographic axes but with different orientations of the polymer chains with respect to the substrate surface. RI-P(NDI2OD-T2), though exhibiting a rather similar LUMO structure and energy compared with the regioregular counterpart, displayed a very different packing structure characterized by the formation of ordered stacks along the lamellar direction without detectible π-stacking. Vertical electron mobilities were extracted from the space-charge-limited currents in unipolar devices. We demonstrate the anisotropy of the charge transport along the different crystallographic directions and how the mobility depends on π-stacking but is insensitive to the degree or coherence of lamellar stacking. The comparison between the regioregular and regioirregular polymers also shows how the use of large planar functional groups leads to improved charge transport, with mobilities that are less affected by chemical and structural disorder with respect to classic semicrystalline polymers such as poly(3-hexylthiophene).