We investigate model order reduction (MOR) strategies for simulating unsteady hemodynamics within cerebrovascular systems, contrasting a physics-based intrusive approach with a data-driven non-intrusive framework. High-fidelity 3D Computational Fluid Dynamics (CFD) snapshots of an idealised basilar artery bifurcation are first compressed into a low-dimensional latent space using Proper Orthogonal Decomposition (POD). We evaluate the performance of a POD–Galerkin (POD–G) model, which projects the Navier–Stokes equations onto the reduced basis, against a POD–Reservoir Computing (POD–RC) model that learns the temporal evolution of coefficients through a recurrent architecture. In the present work, the introduction of a multi-harmonic and multi-amplitude training signal eliminates the requirement of multiple training signals with different amplitudes and frequencies, and thereby expedites the training process. Both methodologies achieve computational speed-ups on the order of 10^2 to 10^3 compared to full-order simulations, highlighting their potential as robust, efficient surrogates for real-time and accurate prediction of crucial flow properties such as wall shear stress (WSS), even adjacent to the bifurcation zones.