This paper presents a qualitative and quantitative comparison between the finite element and the finite volume methods for the fluid-structure interaction simulation of blood flow through a real stenosed artery. The artery geometry corresponds to a severely stenosed (around 75% lumen reduction) portion of the brachiocephalic trunk, located immediately upstream of the bifurcation of this vessel into the right subclavian and right common carotid arteries. The patient-specific geometry was segmented from medical images of a computerized tomography scanner from an individual with the subclavian steal syndrome. Doppler ultrasound velocity measurements were used to determine and impose patient-specific boundary conditions. The numerical simulations were performed in commercial software, Ansys and COMSOL, with a comparative second order discretization for the pressure, velocity and displacement variables. The results of this research disclosed a reasonable overall agreement between the predicted hemodynamics for both approaches. The finite volume method software (Ansys) proved to be more efficient in computational time and memory requirements.