The P1S has a smaller and simpler display/control panel, a lower resolution camera, no filament sensing, no LIDAR sensor, extruder and nozzle parts in plain instead of hardened steel, no built-in storage besides the SD card.
https://bambulab.com/en/compareI don't have first-hand experience with either printer, but have looked around, as you are now. All reports seem to agree that the print quality and speed is identical betwen the two models, and that the lack of convenience in the P1S is minimal. A few reviewers mentioned that they actually like the simpler display unit of the P1S better than the touch screen of the X1; certainly a matter of personal preference.
My personal conclusion was that I will go with the P1S -- if and when I decide to upgrade my current cheap printer at all.
EDIT: If multicolor printing is your main intended use: The 4x filament changer seems to work well, according to all reports, but wastes a surprising amount of filament. In a multi-colored print it needs to switch filaments for every layer, of course, and it takes quite a bit of runway and the some "buffer" filament feed every time.