Semiconductor nanowire arrays have been identified as a promising platform for future light emitting diodes (LEDs), for example, due to the materials science freedom of combining lattice-mismatched materials in them. Furthermore, the emission of light from nanowires can be tailored by designing their geometry. Such tailoring could optimize the emission of light to the top side as well as enhance the emission rate through the Purcell effect. However, the possibility for enhanced light extraction from III-V nanowire arrays over a conventional bulk-like LED has not been investigated systematically. Here, we use electromagnetic modeling to study the emission of light from nanowire arrays. We vary both the diameter of the nanowires and the array period to show the benefit of moving from a bulk-like LED to a nanowire array LED. We study the fraction of light emitted to the top air side and to the substrate at wavelength λ. We find several diameter-dependent resonant peaks for which the emission to the top side is maximized. For the strongest such peak, by increasing the array period, the fraction of emitted light that is extracted at the top air side can be enhanced by a factor of 30 compared to that in a planar bulk LED. By modeling a single nanowire, we confirm that it is beneficial to place the nanowires further apart to enhance the emission to the top side. Furthermore, we predict that for a nanowire diameter D > λ/2, a majority of the emitted power ends up in the substrate. Our results offer direction for the design and optimization of nanowire-array based light emitting diodes.