MX-P is a hard-sponge version for players who want to have power with shorter movement-technique or need speed without having the best hand- & arm-acceleration. The own catapult of the MX-P version is a little bit higher than the MX-S version, so the speed, maximum-spin and power comes more from the included power of the rubber and you need not so much acceleration of your body (it is not necessary to "activate" the rubber, because it has more build-in-catapult, so you can produce the same spin and power with a shorter and slower technique).
MX-S is a hard-sponge version for players who have a good hand- & arm-acceleration and have a little bit longer movement-technique. The own catapult of the MX-S version is a little bit less than the MX-P version, so the speed, maximum-spin and power comes more from your acceleration of your body (you "activate" the rubber with your longer and faster technique).