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Fabry-Perot antennas (FPA) achieve high broadside directivity due to the simultaneous excitation of a pair of nearly degenerate TE/TM leaky-wave modes using a partially-reflecting surface on top of a ground plane. This partially-reflecting surface can be obtained using a dielectric superstrate or via a capacitive or inductive metasurface (MTS). By using an equivalence between the conventional dielectric superstrate and the MTS-based structures in terms of the dominant TE/TM modes, we show that the use of inductive grid MTSs leads to a directivity enhancement. A higher roll-of in the radiation patterns is achieved as a result of the intrinsic suppression of the spurious leaky wave mode. This suppression is mathematically demonstrated and validated with full-wave simulations. The achieved improvement in more than 1 dB for inductive strip grid based MTS with respect to dielectric based super-layers, for the same frequency band of 2.5%, is verified with measurements. Two prototypes, with the dielectric superlayer and inductive strip grid based MTS, have been fabricated and measured supporting the claim of this work.