This paper reports on molecular dynamics simulations of two hydrated micelles composed of C12E6 and LDAO surfactants. The simulations results provide a quantitative picture of the dynamics of the hydration water at the water/micelle interface. Both the residence time of water near the micelle surface and its retardation with respect to the bulk have been estimated. It is found that the water dynamics is radically different for the two micellar systems and depends on the physical nature of the micelle surface in contact with water. For C12E6 this interface is thicker and presents a stronger hydrophilic character than that of LDAO. Thus, in C12E6, surface water dynamics is 1-2 orders of magnitude slower than that of bulk water, compared with only 18% for the LDAO system. The simulations have also revealed the nature of the rotational landscape experienced by water at the micellar surface: In the C12E6 micelle water rotation occurs in a highly anisotropic space due to confinement of waters at the interface; in LDAO the rotational landscape is instead isotropic. These findings clearly indicate that the slowdown of interfacial water relaxation near complex micelles depends, case by case, on the structural properties of the interface itself, such as the ratio between hydrophobic/hydrophilic exposed regions and on the interface thickness and topography.