The only novelty of Saw III is the theme of forgiveness. The movie plays up the idea that revenge doesn't make people feel better about their past victimization.
I'd love to see some empirical happiness research on this point. I'm willing to believe that forgiving makes people happier than nursing grudges. But I also think it is very likely that - contrary to all platitudes - revenge is a surer and quicker path to the recovery of happiness than forgiveness.
In evolutionary terms, revenge serves the clear function of deterring future offenses against you and your family. Not feeling good about getting payback from those who've done you wrong just doesn't seem evolutionarily stable.
And introspectively, revenge gives closure. Every time you remember the wrong done to you, you'll also call to mind the way you balanced the scales. One of my happiest childhood memories involves a sneak attack with my lunchbox on a kindergarten bully. The pain of the bullying is long since forgotten, but the joy of righting the scales of the schoolyard is still with me.