We investigate a new type of behavior whereby small vesicles orbiting around a larger vesicle in a toroidal electrohydrodynamic flow undergo dynamic angular segregation. Application of a low frequency (similar to 50 Hz) electric field induces aggregation of adjacent unilamellar vesicles near the electrode, in a manner similar to that observed with rigid colloidal particles. For polydisperse vesicle suspensions, however, small vesicles (< 10 mu m) are often observed to "orbit" around larger vesicles (> 20 mu m) in a toroidal electrohydrodynamic flow field. While orbiting, the smaller vesicles gradually segregate into well-defined angular cross sections. Viewed from above, the vesicles appear to form dynamic "bands" at prescribed angles, separated by regions devoid of vesicles. We interpret the angular segregation in terms of induced dipolar interactions, and we propose a model based on point dipoles rotating in a cellular flow field. We demonstrate that the model yields a surprisingly diverse range of vesicle trajectories, including many that are qualitatively consistent with the experimental observations.