I'll add a data point by going through the December 2013 episodes. I didn't break things down as thoroughly as parliboy did (I simply subtracted the Prize Puzzle value from the final totals).
In 22 episodes, there were 7 in which subtracting the value of the Prize Puzzle would have changed the winner of the game.
Regardless of whether it affected the final winner, the contestant who won round three was the ultimate winner in 18 of the 22 episodes, which contributes to the perception that the Prize Puzzle swings the outcome of the game. I theorize that this may partially be because the player who solves the round three puzzle (even if they also won rounds one and/or two) is usually the player in the lead at the end of that round.
