Heavy Rain is definitely top, but Uncharteds and inFamous are certainly close

1.  Does this thread title make anyone else sad?  Seriously, it's just painfiul to read that.

2.  Uncharted.

To be honest I don't think many PS3 games this gen have had truly special gaming story's compared to previous gens, but story's that have been implemented well and/or had emotional impact for me:

• Uncharted 1 & 2: Simple and entertaining stories in both games filled with humour
• Half-Life 2 & Ep 1 & 2: OK, so it was ported poorly, but the storytelling in these games is still top notch and work very well by sticking to the first-person view all the way through. When a cut-scene takes place they really make you feel helpless (especially end of ep 2).
• Heavy Rain: A well-told story with multiple options for user input.
• MGS 4: If you played the older titles, than this really was a special way to round it all off for Solid Snake (made my girfriend cry :P).

Uncharteds, Resistance FOM, MSG4

Among the best:

-BioShock. Absolutely fantastic. The sequel just couldn't create the same empathy for the main character, incredible atmosphere and shocking twist of the first game.

-Assassin's Creed II. Ezio is a great character, and when they can be bothered to flesh it out, the AC story is a brilliant one.

-Uncharted 2: Among Thieves. Not for the story itself (which is standard adventure fare) but for the way in which it was told. The acting never sounded forced, each of the characters had individual personalities, and it served to complement the action instead of slowing it down.

-Heavy Rain. Of course.

-Ratchet and Clank Future: Better storytelling than ever before in the series, really. It dared to be a little less safe and secure.

-Metal Gear Solid 4. No explanation needed, really.

1. Infamous

2. Heavy Rain

3. Metal Gear Solid 4

4. Uncharted 1/2

Valkyria Chronicles has the best story in any game i've played on the PS3. 

Also, Demon's Souls story was pretty good, even though it's not directly shown in the game, it's subtly hinted by NPC's and events that partake in the game. 

MGS4 or Uncharted (1 and 2). Haven't played Heavy Rain yet though. I'll have to pick it up sometime.

uncharted 2

Disgaea 3
Followed by Folklore then probably Demon's Souls. Demon's Souls ranks third for me mainly because of how the story was presented [you pretty much had to discover it for yourself; very few games let me do that these days]. MGS4 would be 3 if it didn't rely so heavily on the past games. Heavy Rain... not sure where to put it but it's probably not in my top 5. Heavy Rain, inFamous and MGS4 are honorable mentions, I suppose.