Through-thickness crystallographic texture gradients may develop in extruded profiles and rolled sheets of aluminium alloys. These texture gradients are often modelled using the crystal plasticity theory in order to predict strain localisation more accurately. In this work, an experimental and numerical study was carried out for a flat extruded profile with texture gradients made of the aluminium alloy AA6063. Uniaxial tension and plane-strain tension specimens were produced from this profile in two orthogonal material directions and heat treated to different tempers to study the role of crystallographic texture and work-hardening on strain localisation. The microstructure, including the orientation, morphology and position of the grains, was obtained from EBSD scans. The plane-strain tension tests were simulated using two crystal plasticity finite element models: the first represents accurately the measured microstructure, whereas the second one only represents correctly the global texture but not the texture gradients and grain morphology, i.e., the grain orientations are assigned randomly. In addition, a coarser model was used to identify the material parameters based on data from the plane-strain tension tests. The simulation results showed that accurate modelling of the microstructure did not influence the simulation results significantly. The model with the same global texture but with random assignment of grain orientations gave similar predictions for both the global stress-strain behaviour and the local deformation patterns.