I played the demo for Heavy Rain back when it first hit the PSN. I was intrigued.  After reading the reviews I've been considering picking it up. However...
 
I knew Quantic Dream had made Indigo Prophecy a few years back, and knew it had generally favorable reviews, so a few weeks back when I saw it on Steam for $3, I picked it up. After playing through it, all I can say is that I absolutely hated it.  Seriously. Like, "I want to mail David Cage a box of dog turds" kind of hatred.

Anyway, I would like to hear from people who've played both Indigo Prophecy and Heavy Rain, how similar are they, as far as gameplay goes?

I would say not so similar that some people weren't more inclined to compare Heavy Rain to games like Shenmue instead of Indigo Prophecy.  Hard to say really.  IP put more time constraints on the player, HR has a bit more openness in the path of the story seemingly.  Heavy Rain never got anywhere near as nuts as IP too, and when it gets a little crazy it's generally more enjoyable.
 
IP had quicktime events where you had to nail every single button press for like 10 minutes.  Heavy Rain never stops the game even if you fail an entire quicktime event.
 
Heavy Rain is definitely the better game, but it's still not perfect.

" @Diamond:  Thanks for the reply! The exceptionally long QT events were definitely what bugged me most about Indigo Prophecy. I wasn't even bad at them, they just got annoying. I'll probably pick Heavy Rain up sometime in the near future. "

Heavy Rain is infinitely better then Indigo Prohepcy.
 
.......It is also infinitely more boring.
 
 Heavy Rain is a thoroughly mediocre, boring thriller with poor voice acting and writing. Indigo Prophecy is a bat shit insane(completely self-serious) story about a man who fights the internet and has sex with his necrophiliac girlfriend.
 
I cannot see why one would possibly hate Indigo Prophecy, but even if you hated this gem, you'll probably won't like Heavy Rain if you have a discerning eye for quality.

 @NTM: I don't remember selecting a difficulty, but I usually do avoid selecting "easy," so that's a possibility.
 
@Akeldama:  Hrm, I don't think so. I play a lot of older games, and my dislike didn't have anything to do with graphics. It was mainly the gameplay and the fact that the story took a dump about halfway though.
 
@immike:  Thanks, I will probably will end up renting, as you suggested. I didn't necessarily find Indigo Prophecy "boring" perse, just aggravating that it gave the illusion of choice, when, aside from a few key times, you were forced to do exactly what the developer wanted you to (mainly, play never-ending games of Simon).

" @CompleteInanity:  Heavy Rain has a really great story. The only problem is that it is a lot like reading an interactive book. You will play through all of the slows and action-packed chapters. It's safe to say that most of the lows are in the beginning, so you should remain intrigued throughout the rest of the game. I'm not sure though, because if you found Indigo Prophecy boring, Heavy Rain isn't exactly completely different. Still, there is really no reason to own it other than as part of your collection. You can finish the game in a rental period easy and you won't feel a need to revisit it really. "

that lady cop had a nice booty.
 
also be weary of stereotypical black cop and chinese people.
 
also get the EU version. it had 1 more extra mini-game.

"get the EU version. it had 1 more extra mini-game. "