Verdict
Almost identical sticker price, dramatically different machines. P1S is enclosed CoreXY — faster, better with ABS/ASA out of the box, AMS-ready. MK4S is open bedslinger — better serviceability, lower failure rate (2.1% vs 3.0%), Prusa's first-class US/EU spare parts ecosystem.
Buy the P1S if: you'll print enclosure-required materials (ABS, ASA, polycarbonate), value speed, want hands-off Bambu Cloud workflow.
Buy the MK4S if: mostly PLA/PETG, planning 4+ year retention, prefer Prusa community and open-source firmware over Bambu's walled garden.