We investigate the capability of directional detectors to probe neutralino dark matter in the Minimal Supersymmetric Standard Model and the Next-to-Minimal Supersymmetric Standard Model with parameters defined at the weak scale. We show that directional detectors such as the future MIMAC detector will probe spin dependent dark matter scattering on nucleons that are beyond the reach of current spin independent detectors. The complementarity between indirect searches, in particular using gamma rays from dwarf spheroidal galaxies, spin dependent and spin independent direct search techniques is emphasized. We comment on the impact of the negative results on squark searches at the LHC. Finally, we investigate how the fundamental parameters of the models can be constrained in the event of a dark matter signal.