Jordan, widely hailed as the best player of all-time and who turns 50 on Sunday, believes it is all about championship rings, while James, 28, thinks that view is a little too simplistic.
The debate has been the chief talking point of reporters and players in the run-up to the National Basketball Association's (NBA) All-Star game in Houston on Sunday.
In an interview on NBA-TV to be aired Monday, Jordan took a swipe at James, saying his one championship could not compare with the five won by Los Angeles Lakers guard Kobe Bryant.
"If you had to pick between the two, that would be a tough choice, but five beats one every time I look at it, and not that he (James) won't get five, he may get more than that, but five is bigger than one."
James, a nine-time All-Star and three-time NBA Most Valuable Player, told reporters covering Sunday's All-Star game that was just Jordan's opinion.
"At the end of the day, rings don't always define someone's career," said James. "If that's the case, I would sit up and here and say (Bill) Russell over Jordan. But I wouldn't.
"Russell has 11 rings and Jordan has six. Or I would take (seven-time NBA champion) Robert Horry over Kobe. I wouldn't do that."
James has been on such a scoring streak comparisons with the game's all-time greats were inevitable.
Before he won his first title last season with the Miami Heat he was generally regarded as a great individual talent but not in the conversation with Bryant, or someone like Jordan, who won six crowns with the Chicago Bulls.
James's record six-game streak of scoring at least 30 points with 60 percent shooting came to an end Thursday but he did manage 39 points (on 58 percent shooting), with 12 rebounds and seven assists in a 110-100 victory over Oklahoma City.
"Jud Buechler (three-time NBA champion with Chicago in the 1990s) has multiple rings," said James. "Charles Barkley doesn't have one ring. He's not better than Charles Barkley.
"Rings don't define a person's career. Patrick Ewing is one of the greatest of all time. Reggie Miller is one the greatest of all time.
"Sometimes, it's the situation that you're in and the team that you're in, but it's also about timing as well."
Washington Post columnist John Feinstein slammed James, saying, "you don't put Horry or Buechler into the conversation, or Steve Kerr - who won five on two different teams."
"The question is, 'As the best player on a team how many championships did you lead your team to?,'" he told Reuters. "Russell is the best winner of all-time and Jordan and Kobe are way ahead of LeBron - for now."
Bryant stepped gingerly around the fray, saying Jordan's "message is winning is above everything else."
"That's what drives him," he said. "Same thing that drives him now, win as many as you can. It's really that simple."
Feinstein said James should have taken the humble route and said of Jordan, "He's right, I have won only one title. When he was 28 he had also won one. I hope I'm fortunate enough to win a few more before I'm done."
While comparisons between the game's greats will endure, the All-Stars in Houston insist no one has reached Jordan's genius.
"Every kid that wanted to play basketball, that could play, that couldn't play, you tried to emulate Michael Jordan," said Miami Heat nine-time All-Star guard Dwyane Wade.
"That's why there will never be another one of him. He was kind of the first of his kind. Everything he did was groundbreaking in a sense.
"He did it with so much flare and so much pizzazz that even today people are still trying to be like Mike."
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