Bejeweled and Panel de Pon are quite different, actually. The only similarity is match-three tile-swapping; I seriously doubt Bejeweled is based on PdP in any conscious way.
Bejeweled is really passive; you match and then wait for new pieces to drop. PdP is heavily time and reflex based; constant pressure from rising tiles and the ability to match and move in between drops makes it an entirely different game.
If there's any popular puzzle game out there that's based heavily on PdP, it the iPhone game Aurora Feint, not Bejeweled.
As for Puzzle Fighter, it's quite unique in that it's not really based on color/tile matching at all; at least, not in the same way that games like Puyo Puyo or Panel de Pon are. The system is really tailored to a 'versus' mode and you can have a lot of crazy, brutal turnarounds.