Rapid identification of damaged buildings after natural disasters or on war areas is crucial to support emergency response and prioritize interventions. Earth Observation constellations provide timely, large-scale coverage, but actionable information is often delayed by data downlink constraints, on-ground processing, and human interpretation. Reducing this latency is essential to improve decision-making responsiveness. In this work, we propose an original AI-based system that enables object-level building damage assessment (localization and damage classification) directly onboard satellites from pre-disaster and post-disaster highresolution optical imagery. Available pre-disaster images are encoded on ground into compact latent representations, transmitted to the satellite, and compared on-board with newly acquired post-event observations. Leveraging AI interpretation capabilities and increasing processing capabilities on-board satellites, the proposed design enables processing directly at the data source, reducing the amount of information to be downlinked while preserving task-relevant content and improving overall system responsivity. We explore the design space through a systematic benchmark of onboard-compatible variants, analyzing the impact of siamese processing, cross-attention, latent-space compression, and robustness-oriented data augmentation. Experiments on xBD dataset demonstrate reliable and robust damage assessment under misalignment, with minimal performance degradation under strong compression.