Patient-specific blood pressure values in the human aorta are an important parameter in the management of cardiovascular diseases. A direct measurement of these values is only possible by invasive catheterization at a limited number of measurement sites. To overcome these drawbacks, two non-invasive approaches of computing patient-specific relative aortic blood pressure maps throughout the entire aortic vessel volume are investigated by our group. The first approach uses computations from complete time-resolved, three-dimensional flow velocity fields acquired by phasecontrast magnetic resonance imaging (PC-MRI), whereas the second approach relies on computational fluid dynamics (CFD) simulations with ultrasound-based boundary conditions. A detailed evaluation of these computational methods under realistic conditions is necessary in order to investigate their overall robustness and accuracy as well as their sensitivity to certain algorithmic parameters. We present a comparative study of the two blood pressure computation methods in an experimental phantom setup, which mimics a simplified thoracic aorta. The comparative analysis includes the investigation of the impact of algorithmic parameters on the MRI-based blood pressure computation and the impact of extracting pressure maps in a voxel grid from the CFD simulations. Overall, a very good agreement between the results of the two computational approaches can be observed despite the fact that both methods used completely separate measurements as input data. Therefore, the comparative study of the presented work indicates that both non-invasive pressure computation methods show an excellent robustness and accuracy and can therefore be used for research purposes in the management of cardiovascular diseases.