A detailed analysis of intersubband electron scattering transport in GaAs/AlGaAs quantum cascade lasers (QCLs) is presented, using a full self-consistent rate equation model. Our approach includes all relevant scattering mechanisms between injector/collector, active region and continuumlike states in the cascade structures. In particular, the influence of the Al mole fraction in the quantum barriers on QCLs performance is investigated, by studying GaAs/AlGaAs structures with 33% and 45% Al barrier compositions, respectively. Excellent qualitative and quantitative agreement with recent experimental results at cryogenic and room temperatures is obtained. The model reproduces the gain saturation reported for the 33% Al device, which precludes laser operation at room temperature, and also the much improved room-temperature performance of the 45% Al device, with calculated 300 K threshold current of 17 kA/cm2, and confirms that the superior performance of the 45% Al device is due to suppression of parasitic conduction through continuum states as a consequence of the increased barrier height.