Verdict
Same chassis, same enclosure, same AMS compatibility. The X1C adds: hardened nozzle stock, LIDAR first-layer scan, AI camera failure detection, dual-band Wi-Fi, slightly larger touchscreen. Failure rate measured: P1S 3.0%, X1C 2.7% — the AI detection earns its keep on long prints (catches spaghetti at hour 2 of a 12-hour print).
Buy the P1S if: mostly PLA/PETG, prints under 8 hours, brass nozzle is fine, you'll add a Pi-cam for monitoring DIY-style.
Buy the X1C if: printing PETG-CF/PA-CF (hardened nozzle is mandatory anyway), running 12+ hour prints regularly, or you bill enough that one saved spaghetti-monster covers the price delta within 3 months.