A few requirements to be a good 1 on 1 player.
1. You have to be able to shoot; if all I you can do is back me down or go to the hole, I can defend that no matter how tall you are... because you still have to be able to dribble and a decent perimeter defender can get a big man to pick up his dribble. In that case you have to be able to hit a midrange shot in the defenders face because passing isn't an option.
2. You have to be able to finish at the rim, which means handles are a must. You also can close out a shooter if they are too small or too slow to get to the rim.
3. Size matters, following your shot matters, passing ability does not matter.
4. Good hands and footwork matter and the ability to steal the ball and protect the rim are important.
5. If you can't defend the rim or the perimeter then no matter how well you shoot, or get to the rim you're not going to be a great one on one player.
So that said, I'll think Kevin Durrant would beat Michael Jordan one on one. He's a 7 footer that can score anywhere, would be able to rebound over MJ , could post him up, and is one of the greatest shooters in NBA history.
Hard to argue against MJ... but a 7 footer with MJ like skills... hmm
Lebron... he's Magic like.. but he's not a world class shooter.. He'd win his share, but I'm not sure he's better than Durrant one on one.. He's certainly a better team player because of his passing skills and ability to play more than one position on defense
Karl Malone... how do you stop him on offense... how do you get to the rim on him? But he didn't make his career on one on one.. at least not like Durrant and MJ
Charles Barkley... just a thought... hard to stop.. had all the offensive tools and ability to close out on the perimeter and rim
Someone said Bird... he's out because he couldn't stop the dribble drive and he'd have to overcompensate
Someone said Magic (my personal hoops hero, I have his autographed jersey in my office) ... was a very mediocre shooter.. (someone mentioned he could shoot the 3.. notsomuch.. that was the job of Byron Scott and Michael Cooper)
For BYU
Someone mentioned Jimmer... could he play defense? Could he get to the rim one on one against a Danny Ainge in his prime or a Cosic? (no)
I think a darkhorse for best one on one player would be Michael Smith. He had handles, he was tall enough to rebound and back you down, and was a great shooter. His defense was meh, but he had height to close out at the rim and make you one dimensional. (He would dominate Arajou for example... while Jimmer vs Arajuo may have been a stalemate)