The difference in two-dimensional electron gas (2DEG) mobility between single-heterostructure (SH) and double-heterostructure (DH) AlGaN/GaN/(AlGaN) high electron mobility transistors (HEMTs) has been attributed to a variety of scattering mechanisms and physical effects within these devices. In this article, we aim to elucidate the origins of the change in mobility between SH and DH HEMTs, and identify the scattering mechanisms responsible for limiting the mobility in various device structures. To this end, we use a comprehensive numerical low-field mobility modeling framework to analyze the dependence of 2DEG mobility on temperature, Al content in the AlGaN buffer, and thickness of the GaN channel, also validating our simulation results with available experimental data. We show that reports of superior high-temperature mobility in DH HEMTs can be explained by a decrease in polar optical phonon (POP) scattering rates due to lower 2DEG density and in spite of the stronger quantum confinement. On the other hand, reports of lower mobility in DH HEMTs compared with their SH counterparts can be attributed to stronger alloy scattering in structures without an AlN spacer layer, or to an increase in POP scattering in structures with an AlN spacer having similar 2DEG densities, while the differences in interface roughness and dislocation scattering due to the change in crystal quality play only a limited role.