I think this all depends on the type of organisation you work for. Most of the organisations I have worked for have all been Ps. Strangely enough, most of the managers I have had been Js. I think if you are an SP it's a bit easier as you can get rid of that nagging boss by showing them your progress so far. It's a bit harder for NPs as I'm only likely to pull the rabbit out of the hat at the last minute....and it's usually got bells on too :P
All the J types of organisation (mainly private sector) I have not taken to that well at all and have usually left within a couple of months with blood pouring out of my eyes.
I think if your line of work is more "touchy-feely" like Healthcare or charity work (which I think is the best for me, inceidentally) then Ps are more likely to flourish. I think to say flatly that P's struggle at ANY kind of work is a bit of a cop-out
With the evolving technology we have to hand I think that P's are starting to come into there own a bit more and it certainly does frustrate those who like their meetings and illogical deadlines. I've always wanted to make the way I work something comfortable that I can put on when I want to. When I have had J bosses, working life has been more like desert survival. I'm constantly throwing in meat (fancy graphs, logical theories, creating meetings(!)) for the J Lion bosses to feed on whilst I can grapple with what I value as important, interesting and probably useful and meet the usually arbitrary deadline without constant interruption.
I now am self-employed and my work life has never been happier. I highly recommend it if you can!