Verdict
K1 is $100 cheaper, runs Klipper, and is fully open. P1P brings AMS Lite ecosystem and a lower failure rate (3-4% vs 6-7% on stock K1). Klipper-tuned K1 closes the gap to about 4.5%.
Buy the P1P if: production work where reliability earns $200/year easily; AMS multi-color matters; you don't enjoy tuning.
Buy the K1 if: you enjoy Klipper customization, want input shaper tuning out of the box, $100 saved today wins over reliability gains.