For the life of me I cannot.
I can tell the difference between salted and non-salted, sugared and not, but organic versus regular? No.
I tried it today. I got suckered into buying a carton of freshly ground organic PB at the market. Took it home and did a blind comparo with my favorite jar of Jif.
Tasted them side-by-side it with bread, apple slices, celery sticks, crackers, and of course straight up. Nothing. No difference to this (untrained?) palate whatsoever.
Can you taste a difference? If so, what's the difference you're tasting?