Barnum is a lovely, clever musical from the early 80s... and yes it is also about PT Barnum's life... but it also took a showbiz filter to the story and approach and score, and by no means did it tackle the really interesting and dark/conflicting stuff in Barnum's actual life story - not to the degree or in the fashion that modern *film* audiences and critics would have wanted. I guess, at least the score to Barnum doesn't sound like generic pop songs from the early 2000s, so in that sense it would be better suited?
I haven't yet seen The Greatest Showman but I do not think a film of Barnum would have fit the bill either.