We study the electrophoresis of metal-dielectric Janus particles with dipolar director symmetry in two nematic liquid crystals (LCs) having the same sign of conductivity anisotropy (Δσ) but opposite signs of dielectric anisotropy (Δε). The applied ac electric field is parallel and perpendicular to the director for positive and negative dielectric anisotropy LCs, respectively. We show that the Janus dipolar particles propel faster than the non-Janus dipolar particles in both LCs. The propelling speed of the Janus dipolar particles is also significantly higher compared to the quadrupolar Janus particles studied previously. We map the electroosmotic flow fields surrounding a Janus dipolar particle using microparticle image velocimetry (μ-PIV) and show that the flow on a metal hemisphere is stronger than that on a dielectric hemisphere. Altogether, Janus dipolar particles demonstrate efficient electrophoresis compared to both Janus and non-Janus quadrupolar particles. These findings may be useful for applications in active matter, microrobotic and microfluidic devices.