In this article, we have presented calculations of the DC and RF characteristics in comparable AlGaN/GaN and AlGaAs/GaAs HEMTs. The sheet charge density calculations for different gate biases are made using a self-consistent solution of the Schroedinger and Poisson equations. The carrier mobility in the GaN HEMT is extracted from previous Monte Carlo simulations. A quasi-2D model is then used to calculate the drain-current voltage characteristics. The effects of the spontaneous and piezoelectrically induced polarization fields in the AlGaN/GaN HEMT are incorporated into the model by the boundary condition at the hetero-interface. That is the electric displacement must be continuous at the hetero-interface. The model used to characterize the AlGaN/GaN HEMT device is based on a nonlinear polarization model since the macroscopic polarization of nitride alloys is indeed nonlinear as a function of composition. Since a fair comparison of the GaAs and GaN HEMTs requires comparable device structures, we have chosen a device structure for which experimental data are available for GaAs. Unfortunately, no experimental data for this particular structure in GaN exists. Therefore, the model is calibrated for the GaAs calculation to experimental data. Previous calculations were made comparing the GaN calculations to experiment but for different structures. Nevertheless, excellent agreement was obtained between the model and experiment for GaN HEMTs indicating that the model can be successfully employed to the study of GaN HEMTs. Using this model, we have examined six different performance measures for GaN and GaAs HEMTs. The six performance measures are the sheet carrier concentration, capacitance-voltage characteristics, maximum drain current at similar gate and drain bias, pinch-off voltage, transconductance and cutoff frequency. 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 due to a significantly larger sheet charge induced by the polarization field at the hetero-interface. On the other hand, the maximum transconductance in the GaAs device is higher than that in the GaN device. This is because the low-field mobility in the GaAs HEMT is significantly larger than that in the GaN HEMT. Also increments of the sheet charge in the 2D channel with respect to a variation of the gate voltage (DQ2DEG/DVg) in the GaAs device are higher than that in the GaN device. Both of these two factors cause a higher peak transconductance in the GaAs device. The maximum cutoff frequency is very close in these two devices since the GaAs device has a larger Cgs corresponding to its peak gm. However, the transconductance in the GaN device decreases slowly as the gate voltage switches to a forward bias. This indicates that the GaN device can be employed in a larger voltage swing. Consequently, the GaN HEMT exhibits the potential for high power and high frequency applications.