In this paper, the blood transport has been investigated using the single- and the two-phase methods. In the two-phase Euler-Euler approach, the blood is represented by two interpenetrating continua where the dispersed red blood cells (RBCs) of non-Newtonian characteristics are suspended in the continuous Newtonian plasma. The results of the two-phase model, where the RBC's phase is assumed to be Carreau-Yasuda fluid, are validated against the experimental data. Furthermore, comparative analyses were performed in two patient-specific aneurysms, which indicated that for a given pulsatile flow rate, the two-phase blood approach is vitally advantageous over the single-phase assumption, and revealed a deeper inflow penetration, more complex flow structures and denser flow diversion zones in the aneurysm sac. It was obvious that the high OSI values calculated by the two-phase model covered much wider regions than the values predicted by the single-phase model. It was equally crucial that these regions coincided with the TAWSS values lower than the threshold that the single-phase approach can predict. Apparently, the single-phase model failed to spot sites of high rupture risk. The results were further exploited to identify the RBCs aggregation regions as, for example, the concave structures and narrow paths in the saccular aneurysms, for their possible use as the precursors of the thrombus formation.