Grating-based x-ray imaging systems are of two categories: interferometric and non-interferometric. This work focuses on the angular sensitivity of the phase-stepping-based non-interferometric setup. First, a numerical model of the system is developed and verified with experimental results. Then, an existing system is optimized and verified by comparison with biological sample experiments. The results are also compared with those of a Talbot-Lau interferometer. Finally, an analytical formula of the system sensitivity is derived and limitations of the setup are discussed.