Beckham, who left United for glamour clubs Real Madrid, LA Galaxy, AC Milan and finally Paris St Germain; Scholes, who had he ever left United would probably have gone to unfashionable Oldham, the side he supports and where he can sometimes be seen among the fans.
Let's be clear - Beckham was a great player. You don't win as many honours and caps as he did without being able to play a bit. But he didn't become the world's best-known footballer by once being the world's best footballer. Or even world-class.
Some thought otherwise: He was twice runner-up in Fifa's World Player of the Year award, in 1999 and 2001, although it's debatable he was even the second-best player at his club, never mind the planet.
But true world-class players lift their teams to unprecedented success. A good gauge of a player's impact is how their former and current clubs fare. Beckham's transfer from Manchester United to Real Madrid in 2003 is illustrative.
When he moved to Spain, Real were the world's top club, having won the Champions League three of the previous six seasons. In Beckham's four years in Madrid, Real claimed just one trophy - La Liga in his last season.
Ferguson moved him on because he believed Beckham's off-field exploits were compromising his on-field effectiveness. Ferguson never had any such qualms about Scholes, who helped United to 11 more trophies in the decade after Beckham left. Scholes is now 38 but such is the esteem in which he is held by Ferguson, it came as no surprise that he selected Scholes to start his final match in charge at Old Trafford against Swansea last weekend.
While Beckham clearly has the greater profile, Scholes has been lauded more by peers such as Thierry Henry and Zinedine Zidane. Perhaps the comments of Xavi, the world-class Barcelona and Spain midfielder, best sum up his abilities.
"For me, and I really mean this, he's the best central midfielder I've seen in the last 15, 20 years," said Xavi. "He's spectacular, he has it all: the last pass, goals, he's strong, he doesn't lose the ball, vision. If he'd been Spanish, he might have been rated more highly."
Had Scholes shared Beckham's thirst for self-promotion, he would be rated far more highly. Given his desire to shun the spotlight, he probably doesn't care, but Paul Scholes deserves to be remembered among the best of his generation.