I played the demo for Heavy Rain, and while the style and presentation were intriguing, it was all drowned out by absolutely terrible acting and dialogue. All (but one) of the supposedly "American" characters are clearly played by French actors, and the creators assumed actual Americans would be too stupid to notice. Speaking of the creators, the guy behind it, David Chase, is one of the most fanatically egotistical douchebags in the gaming industry, and the company of characters like Tomonobu Itagaki and Dennis Dyack, that's saying something. It also has one of the worst cases of the Uncanny Valley that I've ever seen in a retail game. And finally, I hear tell (though I cannot personally confirm) that it contains massive plot holes.
That's my two cents on the game, anyway. But if people are looking for an intensely narrative-focused game with a genuinely mature storyline, you know what they should play? Silent Hill: Shattered Memories, one of the most under-appreciated titles this gen. I've heard Alan Wake is pretty good as well, but not having a 360 I can't verify.