While CTA is an established clinical gold standard for imaging large cerebral arteries and veins, an important challenge that currently remains for CTA is its limited performance in imaging small perforating arteries with diameters below 0.5 mm. The purpose of this work was to theoretically and experimentally study the potential benefits of using photon counting detector (PCD)-based CT (PCCT) to improve the performance of CTA in imaging these small arteries. In particular, the study focused on an important component of the CTA image package known as the maximum intensity projection (MIP) image. To help understand how the physical properties of a detector quantitatively influence the MIP image quality, a theoretical model on the statistical properties of MIP images was developed. After validating this model, it was used to explore the individual and joint contribution of the following detector properties to the MIP signal-to-noise ratio (SNR): inter-slice noise covariance, spatial resolution along the z direction, and native pixel pitch along z. The model demonstrated that superior slice sensitivity, reduced inter-slice noise correlation, and smaller native pixel pitch along z provided by PCDs lead to improved vessel SNR in MIP images. Finally, experiments were performed by scanning an anthropomorphic cerebral angiographic phantom using a benchtop PCCT system and a commercial MDCT system. The experimental MIP results consistently demonstrated that compared with MDCT, PCCT provides superior vessel conspicuity and reduced artifactual stenosis.