The Circle of Willis (CoW) is a ring-like structure of blood vessels at the base of the brain that distributes arterial blood to the cerebral mass. 1D and 3D CFD models of the CoW have been created to simulate clinical scenarios, such as occlusions in afferent arteries and absent circulus vessels. Both models capture cerebral haemodynamic auto-regulation using a Proportional-Integral controller to modify efferent artery resistances to maintain optimal efferent flowrates for a given circle geometry and afferent blood pressure. The models can be used to identify at-risk cerebral arterial geometries and conditions prior to surgery or other clinical procedures. The 1D model is particularly relevant in this instance, with its fast solution time suitable for real-time clinical decisions and scenario testing, as long as it captures the necessary details as a 3D model would. Results show excellent correlation between models for the transient efferent flux profile with differences less than 5%. The assumption of strictly Poiseuille flow in the 1D model allows more flow through the geometrically extreme communicating arteries than the 3D model. This discrepancy was overcome by increasing the resistance to flow in the ACoA in the 1D model to better match the resistance seen in the 3D model, significantly improving correlation of the results.