Semiconducting carbon nanotubes^{1, 2} and nanowires³ are potential alternatives to planar metal-oxide-semiconductor field-effect transistors (MOSFETs)⁴ owing, for example, to their unique electronic structure and reduced carrier scattering caused by one-dimensional quantum confinement effects^{1, 5}. Studies have demonstrated long carrier mean free paths at room temperature in both carbon nanotubes^{1, 6} and Ge/Si core/shell nanowires⁷. In the case of carbon nanotube FETs, devices have been fabricated that work close to the ballistic limit⁸. Applications of high-performance carbon nanotube FETs have been hindered, however, by difficulties in producing uniform semiconducting nanotubes, a factor not limiting nanowires, which have been prepared with reproducible electronic properties in high yield as required for large-scale integrated systems^{3, 9, 10}. Yet whether nanowire field-effect transistors (NWFETs) can indeed outperform their planar counterparts is still unclear⁴. Here we report studies on Ge/Si core/shell nanowire heterostructures configured as FETs using high- dielectrics in a top-gate geometry. The clean one-dimensional hole-gas in the Ge/Si nanowire heterostructures⁷ and enhanced gate coupling with high- dielectrics give high-performance FETs values of the scaled transconductance (3.3 mS m^-1) and on-current (2.1 mA m^-1) that are three to four times greater than state-of-the-art MOSFETs and are the highest obtained on NWFETs. Furthermore, comparison of the intrinsic switching delay, = CV/I, which represents a key metric for device applications^{4, 11}, shows that the performance of Ge/Si NWFETs is comparable to similar length carbon nanotube FETs and substantially exceeds the length-dependent scaling of planar silicon MOSFETs.