Foveation can be defined as the organic action of directing the gaze towards a visual region of interest, to acquire relevant information selectively. With the recent advent of event cameras, we believe that taking advantage of this visual neuroscience mechanism would greatly improve the efficiency of event-data processing. Indeed, applying foveation to event data would allow to comprehend the visual scene while significantly reducing the amount of raw data to handle. In this respect, we demonstrate the stakes of neuromorphic foveation theoretically and empirically across several computer vision tasks, namely semantic segmentation and classification. We show that foveated event data has a significantly better trade-off between quantity and quality of the information conveyed than high or low resolution event data. Furthermore, this compromise extends even over fragmented datasets. Our code is publicly available online at: github.com/amygruel/FoveationStakes DVS/.