I go with RDR, along with many others for the simple reason: It's unique. Sure the whole 'hunt down a man find your family' thing isn't, but the setting, the atmosphere, the mechanics (look at the difference between RDR and GTA IV, massive improvement) the multiplayer. It's all very unique.
The reason people think the story was impressive is because it actually makes you feel something for the character. There are games out there were character(s) die, yet the gamer doesn't give two sh*ts. The story in RDR is capturing.
You also don't need to play it to form opinion on what game appeals to you, I don't say that to negate playing it hands on, but there's enough info and visuals out there to put two and two together, I plan to own them all!
Red Dead Redemption is my favorite game of all times! Even though I've only played through the story once, I loved every minute of it and would play it again if I had the time. The multiplayer was great, too. a huge step in the right direction from GTAIV's MP mode, which I also loved.
Couldn't get into LA Noire, too slow for me. I only got about 6 hours in.
Max Payne 3 is great, Multiplayer is not perfect but, another step in the right direction with all the grinds and loadouts adn how they handled bullet time. Story mode is linear but cinematic (taking a lot of cues from Tony Scott's "Man on Fire"), but still has replay value and is a perfect continuation of Max's messed up story.
But all around RDR is the best R* game to-date IMHO.