InGaN-based blue light-emitting diodes (LEDs) with different quantum well (QW) thicknesses were grown on freestanding GaN substrates with low threading dislocation densities (TDDs) and on c-plane sapphire substrates. In the case of thin QWs of 3 nm in thickness, the external quantum efficiencies (EQEs) of LEDs on GaN substrates, as well as those on sapphire substrates, decreased with increasing forward current, indicating that carrier localization is in play on both types of substrates. For thicker 5-nm-thick QWs, the EQEs of LEDs grown on GaN substrates improved at high current densities, while those on sapphire substrates decreased even at low current densities. The LED with 5-nm-thick QWs on the GaN substrate mounted p-side down and molded with epoxy showed EQE as high as 26% at 125 A/cm2. Cathodoluminescence observations of the active layers on GaN substrates revealed that the expansion of nonradiative areas related to TDDs, which are responsible for the deterioration of the EQE of the LED on the sapphire substrate, had been suppressed.