A comparative assessment of AlGaN/GaN high-electron-mobility transistors (HEMTs) grown by molecular beam epitaxy on silicon and sapphire substrates has been carried out. Large-area power GaN HEMTs with identical device dimensions were fabricated on both substrates. A thicker AlN buffer layer was used for the GaN HEMT on silicon to achieve similar quality and uniformity of GaN epitaxy for rational comparison with that grown on sapphire. Direct-current analysis and physical characterization were carried out to understand the performance of the devices. Mathematical measurement of the instability of the current-voltage (I-V) characteristic at high applied drain bias was carried out to evaluate the performance of both devices. An improved two-dimensional (2D) analysis of the I-V characteristic was performed from a thermal perspective including appropriate scattering effects on the 2D electron gas mobility. The experimental and analytical studies were correlated to reveal the effects of temperature-sensitive scattering phenomena on the mobility as well as on the I-V characteristic at high drain bias in terms of lattice thermal heating. It is observed that the HEMT on Si has improved stability compared with sapphire due to its weaker scattering phenomena at high drain bias, associated with its thermal conductivity. Simulation of 2D thermal mapping was also carried out to distinguish the hot-spot regions of the devices. The comparable electrical performance of these devices illustrates the viability of AlGaN/GaN HEMTs on Si(111) to achieve low-cost stable devices with better thermal power handling for high-voltage applications.