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We compare the temperature dependence of optical and electrical characteristics of commercially available GaN light-emitting diodes (LEDs) grown on silicon and sapphire substrates. Contrary to conventional expectations, LEDs grown on silicon substrates, commonly referred to as GaN-on-Si LEDs, show less efficiency droop at higher temperatures even with more threading dislocations. Analysis of the junction temperature reveals that GaN-on-Si LEDs have a cooler junction despite sharing identical epitaxial structures and packaging compared to LEDs grown on sapphire substrates. We also observe a decrease in ideality factor with increase in ambient temperature for GaN-on-Si LEDs, indicating an increase in ideal diode current with temperature. Analysis of the strain and temperature coefficient measurements suggests that there is an increase in hole transport efficiency within the active region for GaN-on-Si LEDs compared to the LEDs grown on sapphire, which accounts for the less temperature-dependent efficiency droop.