In this article, we explore, experimentally, the impact of band-to-band tunneling on the electronic transport of double-gated WSe2 field-effect transistors (FETs) and Schottky barrier tunneling of holes in back-gated MoS2 FETs. We show that by scaling the flake thickness and the thickness of the gate oxide, the tunneling current can be increased by several orders of magnitude. We also perform numerical calculations based on Landauer formalism and WKB approximation to explain our experimental findings. Based on our simple model, we discuss the impact of band gap and effective mass on the band-to-band tunneling current and evaluate the performance limits for a set of dichalcogenides in the context of tunneling transistors for low-power applications. Our findings suggest that WTe2 is an excellent choice for tunneling field-effect transistors.