We present a theoretically based comparison of the DC and RF performance between AlGaN/GaN and AlGaAs/GaAs high electron mobility transistors, HEMTs, with the same geometric structure. The model for the AlGaN/GaN device includes a nonlinear polarization formulation of the strain polarization fields. The calculation of the drain-current voltage characteristics are made using a quasi-two-dimensional model based on a self-consistent charge control and field-dependent mobility model. The field-dependent mobility in the GaN HEMT is obtained from Monte Carlo simulation while a standard model is chosen for the GaAs HEMT. The model is found to agree well with experimental measurements made for both GaN and GaAs devices. It is found that the maximum drain current and the magnitude of the pinch-off voltage in the GaN device are larger than those in the GaAs device. However, the maximum transconductance in the GaAs device is higher than that in the GaN device. The capacitance-voltage characteristics and current gain cutoff frequency are also computed.