I own a Phantom and a P-01. I also happen to have a spare P-01 slide stop as a back up part (same one you show). The P-01 slide stop fits and functions in the Phantom and the right tip is perfectly flush with the frame, whereas the tip of the Phantom slide stop protrudes 3mm. The P-01 slide stop dry cycles and locks back the slide on an empty magazine like normal (did not fire it). The inner lug on the P-01 slide stop is about 0.7mm shorter than the Phantom slide stop, so it has that much less purchase on the mag follower; it does not slide off the follower, but there is slightly less purchase. I suppose the P-01 slide stop would have better bullet clearance, but that is not a problem with the Phantom slide stop.
I prefer the stock Phantom slide stop as the protruding tip makes it easier to field strip with any (non-marring) flat surface tool. With the P-01 slide stop, one needs a narrow non-marring tool (like the tip of the red plastic cleaning rod) to push it out.
