Complementary metasurfaces composed of randomly-placed arrays of aligned rods or slits are fabricated out of giant magnetoresistance Ni81Fe19/Au multilayers (MLs), a material whose optical properties change under the application of an external static magnetic field. The two metasurfaces are studied from both the experimental and theoretical viewpoints. The induced magnetic modulation (MM) of both the far-field signal and the resonant near field, at the rod/slit localized surface plasmon frequency, are found to obey the Babinet's principle. Furthermore, the near-field MM is found to be higher than the far-field counterpart. At resonance, both arrays show spots with high values of the magnetic modulated intensity of the electric near field (MM hot-spots). We show that this high magnetic modulation of the near-field intensity is very promising for the future development of high sensitivity molecular sensing platforms in the Mid- and Far-IR, using Magnetic-Modulation of Surface-Enhanced Infrared Absorption (MM-SEIRA) spectroscopy.