In this paper, we study the band structures of Si and InAs nanowires based on a first-principles calculation and project performance potentials of Si and InAs nanowire field-effect-transistors (NWFETs) by using a semiclassical ballistic transport model. We demonstrate that the device performance of InAs NWFETs strongly depends on its cross-sectional dimension and gate oxide thickness. In particular, InAs NWFETs unexpectedly indicate lower current drivability than Si NWFETs as the gate oxide thickness is extremely scaled down to 0.5 nm in the ballistic limit. We discuss the mechanism in terms of operation in quantum capacitance limit (QCL). We also demonstrate that the advantage in the lower power operation with InAs NWFETs reduces when the devices operate in the QCL or higher subbands with a heavier transport effective mass participate in the transport.