He was trained by the first and second hokage so he has immense battle experience.
That and his 1000 jutsus, including his bad-ass summon enma, and possibility of a sage mode would allow him to defeat any of those other kages.
It is a fact that the Hokages were the strongest shinobi of their time, and kishi wouldn't state this unless he has already planned for them to be very OP beyond other village ninjas.
This is all true.
He is the only known character with a perfect 5 in nin, tai, and gen; then there's his incredible intellect which was shown recently, being able to deduce the strengths and weaknesses of his opponent's ability by only seeing it one time using a ploy. He also may had learned Shiki Fuujin from seeing Minato use it one time. Truly deserving if his "Professor" monicker.
Hiruzen is very likely to show more before the war in over, perhaps giving him pt.2's power inflation and showing why he was considered so powerful... yet this is still 70 year old Hiruzen who wasn't as fast or strong as he used to be in his prime. In fact, Hiruzen was fast enough to avoid a fatal shot from Obito's initial attack with it only hitting his shoulder, now if he were younger it may had never touched him.