Blood flow in the carotid arteries is usually laminar, but can undergo laminar-turbulent transition in the presence of a high-grade stenosis. In this study, pulsatile flow in a patient-based stenosed carotid artery bifurcation was examined using both large eddy simulation (LES) with dynamic Smagorinsky eddy viscosity model, and a Reynolds-averaged Navier-Stokes (RANS) method with a transitional version of the shear stress transport (SST-Tran) model. In addition, an experimental phantom was built for the same bifurcation geometry and velocity measurements were made using particle image velocimetry (PIV). Comparisons with PIV measurements of axial velocity profiles demonstrated that both SST-Tran and LES predicted the experimental results fairly well, with LES being slightly superior. Furthermore, LES predicted cycle-to-cycle variations in the region where transition to turbulence occurred, indicating the unsteady nature of turbulence transition. On the other hand, the SST-Tran model was able to capture important flow features observed in the PIV experiment, demonstrating its potential as a cost-effective alternative to LES for haemodynamic analyses of highly disturbed flow in diseased arteries.