Satellite imagery plays a crucial role in monitoring changes happening on Earth's surface and aiding in climate analysis, ecosystem assessment, and disaster response. In this paper, we tackle semantic change detection with satellite image time series (SITS-SCD) which encompasses both change detection and semantic segmentation tasks. We propose a new architecture that improves over the state of the art, scales better with the number of parameters, and leverages long-term temporal information. However, for practical use cases, models need to adapt to spatial and temporal shifts, which remains a challenge. We investigate the impact of temporal and spatial shifts separately on global, multi-year SITS datasets using DynamicEarthNet and MUDS. We show that the spatial domain shift represents the most complex setting and that the impact of temporal shift on performance is more pronounced on change detection than on semantic segmentation, highlighting that it is a specific issue deserving further attention.