I know that Neo made different choices when compared to the other Ones. I know that those choices, though uncompromising to a dangerous extent, led to a different turn of events. But what was different about Neo? When he went to the Oracle, he had made the choice but wasn't aware of it. It seemed that the matter of choice here was crucial and Neo unknowingly made the right ones. Now why is that? I mean what is it about him that made him who he was?
The other ones WERE Neo. I think that this is the most overlooked or rather poorly understood portion of the Architect scene. "Though the process has altered your consciousness, you remain irrevocably human". This means that they have some how kept his mind through each of the Matrix reboots and reinserted it into a body each time when the task of the "one" needs facilitating. His soul was changed through each experience. Also, he loved Trinity in this version and she didn't exist in the other versions of the Matrix.
"He was aware that his predecessors had chosen to let Trinity die."
Negative. Trinity never existed in the other versions of the Matrix or Zion.
This segment of dialogue between Neo and The Architect points out one key way Neo differed from his previous incarnations (emphasis added by me):
The Architect: The function of the One is now to return to the source, allowing a temporary dissemination of the code you carry, reinserting the prime program. After which you will be required to select from the matrix 23 individuals, 16 female, 7 male, to rebuild Zion. Failure to comply with this process will result in a cataclysmic system crash killing everyone connected to the matrix, which coupled with the extermination of Zion will ultimately result in the extinction of the entire human race.
Neo: You won't let it happen, you can't. You need human beings to survive.
The Architect: There are levels of survival we are prepared to accept. However, the relevant issue is whether or not you are ready to accept the responsibility for the death of every human being in this world.
The Architect presses a button on a pen that he is holding, and images of people from all over the matrix appear on the monitors.
The Architect: It is interesting reading your reactions. Your five predecessors were by design based on a similar predication, a contingent affirmation that was meant to create a profound attachment to the rest of your species, facilitating the function of the one. While the others experienced this in a very general way, your experience is far more specific. Vis-a-vis, love.
So, one of the key differences between Neo and the previous Ones is his experience with Trinity, falling fully in love with another human being as opposed to simply feeling a "profound attachment" to humanity in general. It was this love for another that led to him making a different choice than the previous Ones, choosing instead to continue resisting the machines and save Trinity as opposed to returning to the source and rebuilding Zion as The Architect designed.
In addition to his experiences with Trinity (see gnovice's answer), Neo was different from the his predecessors because of how his character was designed by the writers:
"..I don't like the idea that I'm not in control of my life."
(In response to Morpheus's question about fate in the first movie)
His defiance against his "fate" was further fueled by the following:
- Being told that his path ends at the Source (conversation with the Oracle at the park in Reloaded) and that he has to follow it
- Being told that "there is no denying purpose" and that he is only "apparently free" (Smith before the brawl in Reloaded)
- Being told that "she is going to die and there is nothing you can do to stop it" (Architect in Reloaded)
In his conversation with the Architect, it is revealed that the One is merely another system of control meant to prevent the entire human race from rejecting the programming of the Matrix. Furthermore, the Architect had just told him that HE WAS DESIGNED to have "a profound attachment to the rest of your species, facilitating the function of the One" -- that he was a pawn made to ensure that the Matrix does not break.
He was aware that his predecessors had chosen to let Trinity die, and that his "fate" was to return to the Source, reinsert the prime program, rebuild Zion and repeat the cycle again. Doing so would mean making choices that the machines wanted him to make -- succumbing to his "fate" as an anomaly.
Because he doesn't like the idea that he's not in control of his life** and that doing what he was supposed to do won't end the war between man and machine, he took the door to his left.
**or maybe because he wanted to make another "how about I give you the finger" moment after the Architect tells him he won't be able to save Trinity
The answer to this question is a simple one. This Neo ended the war between machines and humans. The "others" were not able to bring about peace; destroying Zion each time. This "Neo" also enabled the "programs" to experience love, because of his love for Trinity. It was "love" in the end that brought about the end of the war.
At the end, with the little girl and the Oracle discussing if they would see Neo again, they will, but the next time he appears he will be half-human-half program., not machine. He will be part of the programming of the new matrix; it really was Neo's purpose all along!
He has to be "part" of the matrix to ensure an ever-lasting peace. But we all know peace does not last forever!