I think that, more often than not, LeBron squeaks out a close victory over Jordan.
Since a lot of this is all conjecture predicated upon per-existing notions of how two players, who obviously never played one-on-one in their prime, would match up, this is what I believe:
- I believe that Michael Jordan is the best player ever to play basketball.
- I believe that between Jordan and James, Jordan is the superior defender.
- I believe that Jordan's drive and determination were both greater than LeBron's are.
But here's the thing, for every one of those things that I believe, there are things that I know that puts all of that in context:
- I know that LeBron will at worst be considered one of the fifteen best players ever to play the game. And I know that the gap between Jordan's skills and James' skills isn't the gulf that some might want to believe it is.
- I know that Jordan didn't exactly rack up defensive accolades guarding people like LeBron. That's not to say that he didn't guard elite players, just that he didn't guard players of LeBron's size all that often.
- I know that the idea of Jordan's competitive drive "willing" him to victory in a one-off game is kind of silly. The ethereal notions of "drive" and "determination" are surely something, but they're likely each something that manifests itself over the course of a long season, not in a quick game of one-on-one.
Look, LeBron isn't stupid. At some point he's is going to realize that he can just bully Jordan in the post area, and spend most of his time utilizing his size advantage on offense, rather than relying on jumpers. LeBron is also a good defensive player (as has been noted in answers like the ones by Jonathan Brill
and Dave Hogg
in support of LeBron, and conceded in answers that favor Jordan by User
, and Andrew Miller
). So, on one side, we've got Michael Jordan, the superior player on either side of the ball, but who faces a size mismatch on the defensive end. On the other side, there's a larger LeBron James, whose physical skills give a greater chance of having his defensive skill impact his opponent's offensive outcomes. All James has to do is frustrate Jordan a little bit more than Jordan can frustrate him, and his physical skills give him the toolbox to accomplish that task.
Jordan is, hands down, a better player and I don't know of many people who will dispute that statement. But that doesn't mean he can win any one-on-one match up (nor does losing mean he isn't the best player ever); there will be times that he would just be given an opponent that sneaks through what few cracks he has in his armor. And, in a one-on-one situation, James is one of those opponents.
 I say at worst because there's an outside chance (a very, very small outside chance) that James either never wins another title or never wins a title without Wade and Bosh, and that ends up making us view what will probably be top-five statistics in a diminished light.
 Let's get real for a moment, Jordan won Defensive Player of the Year guarding the likes of Clyde Drexler (6' 7", 210 lbs), Isiah Thomas (6' 1", 180 lbs), Dominique Wilkins (6' 8", 230 lbs), Bernard King (6' 7", 205 lbs), Magic Johnson (6' 9", 220 lbs), etc; all players that had a similar physical stature as Jordan (6'6", 216 lbs). LeBron is two inches taller than Jordan, has thirty to forty pounds on him (and possibly more, given that many people often believe that James is actually heavier than his listed weight), and has a wingspan that is three inches longer than Jordan's. At some point, technical skill can be overcome by sheer physical force, and this is kind of that point.
 And while I wouldn't argue that Jordan was a bad low-post defender, he certainly could be taken advantage of in that area by larger opponents. During the time that both Jordan and Magic were active, Magic posted pretty good numbers against that Bulls. Now, presumably Jordan wasn't checking him every time, but Magic still succeeded more often than he failed against the Bulls. Penny Hardaway, certainly a lesser player than Magic, also saw some measure of success against the Bulls during the time that both he and Jordan were active. Both were players that Jordan would have seen regular time guarding and who both were generally prone to trying to take advantage of size mismatches in the low-post area. And neither were as physically strong or gifted as James.
 I reject the notion that Jonathan puts forth in his answer that James is the better offensive player because he scores more efficiently; James also has had the advantage of playing with two other top-tier offensive options (say what you will about Bosh but in today's NBA, he's top-tier) to not only take the usage load off of him, but who also impact the way defenses scheme against James on offense. Look no further than the recent Roy Hibbert discussion during these playoffs (2013 NBA Playoffs: Should the Pacers have played Roy Hibbert on the last possession of overtime in Game 1 of the Eastern Conference Finals?
) for an example.
 Jordan isn't all that much faster than James, isn't as long as James, and probably can't out jump James (and if he can, it wouldn't be by enough to overcome James' longer wingspan). Oh, and then there's all of this: