GaN-based light emitting diodes encompassed with self-aligned nanorod arrays of three distribution densities were designed and fabricated. Light diffraction behaviors are characterized by considering the radiation profiles as well as the angular spectra of those nanorod structures. We demonstrate that the device with the less regular and less dense nanorod (with a fill factor 0.19) distribution has the highest enhancement factor. As we regard the nanorod arrays as localized photonic crystals, the enhancement is due to a large varying lattice constant as well as the leaky mode operation when the emission wavelength falls within the photonic band-gap. Meanwhile the light emission directionality is more obvious when the guided modes are phase matched to the radiation modes that lie above the cut-off frequency of the Brillouin zone boundaries.