Michael Jordan is the best basketball player of all time. While this is almost unanimously accepted, I think that LeBron would win in a game of one on one. His size, quickness, and strength would be too much for MJ to handle.
I assume we are talking about Jordan in his prime. There is no way that Lebron would beat Jordan in game of one on one. Jordan was the ultimate competitor. His will to win alone would be enough for him. Not to mention that Jordan was unguardable one on one. His can't miss fade away would give Lebron fits. Jordan wins easily.
Lebron's strengths are his post game, driving to the basket and his ability to finish at the rim. All things that Jordan was great at as well. The difference is shooting. MJ is a much better jump shooter. That is key in a game of one on one. Also Jordan had quicker hands and was a 3 time steal champion. All things to help him dominate Lebron in a friendly game of 1on1.
Firstly, let me apologize for missing round two, but I think it is fairly clear that Michael Jordan is the best basketball player of all time. However, that does not mean he is the greatest one on one player of all time. Lebron is s quicker, bigger, and stronger and would defend MJ much better than MJ could defend Lebron. LBJ could simply back MJ down and have his way with him.
Additionally, it is a common misconception that MJ is such a great shooter. Check the stats. He is below average from three point range (and is worse than LeBron from three). I agree that MJ has all the intangibles over LeBron, but I don't think that matters in a game of one on one.
I think MJ would make it close, but final score: LeBron 21,MJ 17