III-nitride-based nanowires are a promising platform for solid-state lighting. III-nitride nanowires that act as natural waveguides to enhance directed extraction have previously been shown to be free of extended defects even on foreign substrates, such as silicon. While the efficiency of nanowire-based light-emitting diodes (LEDs) has been investigated, there has yet to be a comparison of heterostructures based on nanowires grown in different crystallographic directions. We compared the directed external quantum efficiency (EQE) of III-nitride LEDs on silicon based on axial and radial nanowire heterostructures, considering - and -directional nanowires. The directed extraction efficiency was calculated using photonic simulations, and the internal quantum efficiency (IQE) was estimated using the model. We found that -directional axial heterostructures have the highest directed extraction efficiency, due to the strong polarization anisotropy of III-nitrides, and display similar IQE as -directional axial heterostructures. By combining IQE and directed extraction, a range of directed expected EQEs reveal that -directional axial heterostructures have EQEs up to three times that of -directional axial heterostructures, providing guidelines for the design of future nanowire-based LEDs.