We describe the synthesis of hybrid magnetic ellipsoidal nanoparticles that consist of a mixture of two different iron oxide phases, hematite (α-Fe2O3) and maghemite (γ-Fe2O3), and characterize their magnetic field-driven self-assembly. We demonstrate that the relative amount of the two phases can be adjusted in a continuous way by varying the reaction time during the synthesis, leading to strongly varying magnetic properties of the particles. Not only does the saturation magnetization increase dramatically as the composition of the spindles changes from hematite to maghemite, but also the direction of the induced magnetic moment changes from being parallel to the short axis of the spindle to being perpendicular to it. The magnetic dipolar interaction between the particles can be further tuned by adding a screening silica shell. Small-angle X-ray scattering (SAXS) experiments reveal that at high magnetic field, magnetic dipole-dipole interaction forces the silica coated particles to self-assemble into a distorted hexagonal crystal structure at high maghemite content. However, in the case of uncoated maghemite particles, the crystal structure is not very prominent. We interpret this as a consequence of the strong dipolar interaction between uncoated spindles that then become arrested during field-induced self-assembly into a structure riddled with defects.