As others have already pointed out, Hidan and Kakuzu are symbolized by the bishop and rook pieces in shogi. This shows up in the nature of their powers and relationship, specifically in their strengths and weaknesses of their preferred offenses and defenses. One thing I found particularly enlightening was Kakuzu's statement that he can not kill Hidan. This implies that Hidan can not kill Kakuzu either, which it seems likely for him to have tried, given their personalities. Each one's mode of offense is largely useless against the other's mode of defense. Hidan is symbolized by the bishop (which shares the first syllable of his name "Hi") which can move any number of spaces diagonally, but is weak horizontally or vertically. This fits Hidan, with his relatively poor standard ninja skills and his unconventional method of attacking (the damage reflection curse ceremony). Kakuzu, on the other hand, seems to be very straight forward, like the rook which symbolizes him ("Ka"). As the rook moves any number of spaces vertically or horizontally but is weak diagonally, he seems to use powerful but not unusual taijutsu with great strength. So what does this tell us about them? When a rook and a bishop are pitted against each other, they can't really defeat each other without a large of amount of assistance from other pieces; the rook moves out of the diagonal path of the bishop and vice versa. Kakuzu's physical style of offense appears useless against a guy who can have his head cut off and live to talk about it. To defeat Hidan's immortality requires a particular trick, as did defeating his curse ceremony. So why can't Hidan defeat Kakuzu? We've seen Kakuzu's skin change color briefly. My theory is that Kakuzu either can make his skin unbreakable, or can change his body to stone or metal. Either way, Hidan would not be able to draw blood from Kakuzu, and thus would be unable to use his curse ceremony to hurt him.