LeBron James is perhaps the greatest rebounder the small forward position has ever seen. While Larry Bird has had seasons and series with better rebounding stats, James plays in a league with more athletic centers and forwards, and is still able to rack up rebounding stats with ease even in Finals series.
Jordan himself is one of the greatest rebounding guards to ever play the game, though the likes of Oscar Robertson, Magic Johnson and Russell Westbrook have better stats than him.
It is worth noting, however, that Jordan is easily the better offensive rebounder of the two. For the length of their careers, Jordan averages 1.6 offensive rebounds over 15 seasons, while LeBron is averaging only 1.2.
Jordan also focused less and less on rebounding after the initial years of his career. It wasn't one of his priorities once Scottie Pippen rose to be elite at this, while the signing of the greatest rebounder in the history of the game, Dennis Rodman, further reduced the necessity of him going for rebounds.
LeBron's career rebounding rate of 11.1% is better than Jordan's 9.4%, giving him an edge in this category.
Edge: LeBron James