The Vault Dweller was born in a Vault ( duh ) that was the only special thing. He saved the world as a normal man. The Chosen One was a tribal, whom was a tad naive to the world. He was also the Vault Dweller's descendant, those were the only things unique. He destroyed the largest threat the wasteland has ever seen. The Courier quelled a local, fruitless, and stupid quarrel between to powers. In my opinion he pales in comparison to The Vault Dweller and The Chosen One.
Perhaps in achievements, yes, but we're discussing both their power and achievements.
The Courier falls far behind all the others when it comes to achievements. Why? Because the Courier may very well be the first neutral-karma hero we've seen. The Courier likes revenge, he likes profit and his actions are mostly political. It's literally impossible for the Courier to finish his adventure in the Mojave and not have blood on his hands: you either gain bad karma for killing Mr. House or for killing the Brotherhood of Steel. Again, I dunno about FO1 and 2, but this may be a first in the sense that the MAIN QUEST ITSELF forces you to gain bad karma.
The things done by the Vault Dweller, the Chosen One and the Vault Dweller are almost undeniably good. All three of them took out a force that was uncompromisingly aggressive against everyone else. The Courier? He's either helping the Legion, the NCR, House or he's killing off all three. No matter what he does, someone is gonna disapprove of his actions. Many people don't like the NCR taxes or want their bureocratic [censored] in the Mojave, Mr. House isn't really loved by the people of Vegas, Caesar's Legion would enslave and kill many, and there are just SOOOO many things that could go wrong with an Independent Vegas.
So yeah, if we ask who achieved the most, the Courier should be at the bottom of the list. His accomplishments don't really benefit humanity as a whole and it's impossible to please everyone in Vegas. The only thing that would make his actions truly remarkable is if Mr. House really did go on to colonize other planets.
What I was referring to though is that some people say "the LW/Chosen One would wipe the floor with the others because of his power armor and tech," arguing that because the lore of power armor is so strong, the others wouldn't stand a chance. I'm arguing that this could work both for and against the Courier because he's the ONLY protagonist who doesn't utilize Power Armor and STILL manages to survive the Sierra Madre, the Big Empty, the Second Battle of Hoover Dam and likely destroyed a BoS chapter all by himself. The Courier is shown to be incredibly cunning and tough, not because of his equipment or his weaponry, but rather that's just who he is.