The 4Ps sound almost identical to the 4S.
The 4P is the SAME as the 4S except the cable. The 4P was designed with a sensitive cable for mobile mp3/cd players.
The 4S is designed to be used with a headphone amp due to the cable's higher resistance. Headphone amps aren't very practical as even the most mobile headphone amp is a hassle to carry around.
The headphone amp will provide more power to the headphone. Attack & decay will be a little more extreme as there is more power being fed into the headphone. You REALLY have to pay attention in a back and forth
A/B testing. For only the most extreme audiophiles this may be an issue. You'll still get 99.7% of the sound with the 4p vs. the 4S.
Simply put, buy the 4S if you use them at home sitting stationary and are willing to buy an expensive headphone amp.
Buy the 4P if you're mobile. Later, you can convert the 4P to 4S, if this issue is bugging the sh!t out of you.
The 4P is definitely the no-brainer choice for me and my needs. You really are not losing out with anything here. Screw the headphone amp. How impractical!!