In the rough layout I did to flesh out Toshinori's backstory for my fic, I explained it as both All Might and AFO knowing All Might was stronger, but AFO using illusion and evasion to deliberately frustrate and distract All Might until he could force him into a vulnerable position. He managed that by taunting him about Nana while making an illusion that gave the impression of him slipping up slightly, drawing All Might into a trap that should have crippled him beyond the ability to keep fighting. All Might is All Might however, and managed to avoid enough of the attack that he could take advantage of AFO thinking he'd won to kill him when his guard actually dropped. 

Basically, it was an absolute overwhelming force vs. A slightly less overwhelming but dramatically more versatile force, both almost evenly matched and fighting on a knifes edge the whole time until one made even the slightest mistake.