So really, the only benefit to the Director's Cut is it includes the DLC. However, the Greatest Hits version of Heavy Rain was available for $15 around Thanksgiving, and will likely be on sale for that price in the future, so you'd save money buying the regular version on sale and the DLC, if you should chose to get it, separate.
That said, Heavy Rain is amazing. It is QTE heavy, but it's not an action game. It's an interactive story, a modern adventure game, and is a haunting and emotional experience. The music is incredible.