Well, having the PK and the WP I think the WP is the more organic of the the two by quite a way, even with its greater output.
Short list of characteristics:
PK: Chunky, tight as hell, crisp, crunchy mid range, biting highs that level out the mids very nicely, but dont get anywhere near the scream of a miracle man. Modestly powerfull, but it gains push and cuts from its superb mids. Really great thrash rhythm pickup.
WP: Fatter, smoother, heavier, growlier, not as tight (but still very tight by conventional pickup standards). Its a warmer sounding pickup and its quite a bit more powerfull. More compressed. Somewhat more 'liquid' in the high end for leads but its got plenty of definition. Its got a huge low end and quite even mid, bar maybe a touch of additional low mids to give it its growl. Highs are very balanced: this is a heavy pickup, but never a muddy one. Much more versatile, you can use this for any flavour of heavy music and quite a few non-heavy ones.
Edit: personally, I love the painkiller. It does what it does brilliantly. But with it having a more specific sound (ultra-tight, middy, permanently agressive) I'd sway toward the pig for its ability to do many more sounds with authority.