Of coarse this is MY OPINION, and many will dissagree. and i will put this out there i am a little biased just like everyone else and a bit of a fosgate fanboy if anybody hasnt noticed.
I have compared both the new p3 and the new type r side by side, type rs in a cobalt (2 12s) and p3s in a grand prix (2 12s) both same box not sure of the specs but it took us over an hour to get it in the cobalt, i would say maybe 3-4 cubes net. and if im not mistaked around 33 hrtz.
Type r: i thought that it sounded good through all volume levels, but when the lower notes came the p3 had a slight advantage, to my ear, and of coarse there are many factors that could differ from cars i thought that the p3 was quite a bit louder as did the two guys that owned the cars. part of this could be do to the fact the the p3 has a slightly bigger cone.
overall i personally like the p3 it seemed to have more of a "punch"(no pun intended), and the type r seemed to have an overall smother responce, so if you listen to a lot of jazz and such i would go with the type r.