Using TracePro® Monte-Carlo ray-tracing simulations, this paper investigates the improved light extraction efficiency (LEE) obtained by patterning the surface and/or substrate of GaN LEDs with unique three-dimensional micro-cavity patterns. The simulations commence by considering the case of a sapphire-based GaN LED. The effects on the LEE of the micro-cavity dimensions, the absorption coefficient of the active layer, the point source location, and the chip dimensions are systematically examined. Subsequently, the LEE performance of the sapphire-based GaN LED is compared with that of a thin-GaN LED for various surface texturing strategies. In general, the results show that patterning either the surface or the substrate of the LED structure provides an effective improvement in the LEE of both the sapphire-based GaN LED and the thin- GaN LED. For both LED structures, the maximum LEE enhancement is obtained by patterning both the upper surface of the LED and the substrate surface. However, the simulation results indicate that the improvement obtained in the LEE is the result primarily of pattering the upper surface of the LED.