The microscopic dynamics of objects suspended in a fluid determines the macroscopic rheology of a suspension. For example, as shown by Danker and Misbah [Phys. Rev. Lett., 2007, 98, 088104], the viscosity of a dilute suspension of fluid-filled vesicles is a non-monotonic function of the viscosity contrast (the ratio between the viscosities of the internal encapsulated and the external suspending fluids) and exhibits a minimum at the critical point of the tank-treading-to-tumbling transition. By performing numerical simulations, we recover this effect and demonstrate that it persists for a wide range of vesicle parameters such as the concentration, membrane deformability, or swelling degree. We also explain why other numerical and experimental studies lead to contradicting results. Furthermore, our simulations show that this effect even persists in non-dilute and confined suspensions, but that it becomes less pronounced at higher concentrations and for more swollen vesicles. For dense suspensions and for spherical (circular in 2D) vesicles, the intrinsic viscosity tends to depend weakly on the viscosity contrast.