Well, that was the thing that made Rome exceptional .
Er the Romans did not draft their soldiers, they were professional soldiers. They weren't exceptional at all in that area, heck even Babylonians were more exceptional with their draft system. Their armies weren't even that big even if you compare it to Late Medieval standards. What was exceptional with Rome though was integration which gave them a lot of potential manpower.
Correct me if I'm wrong, but wasn't the 6th coalition formed as a direct result of the failure of the Russian war and was the coalition that defeated Napoleon? My Napoleonic wars history isn't the greatest so I could be wrong.
Yes it was, and the quotes authenticity is disputed as in "we don't know if it is actually true he said this", heck Napoleon is even known for liking to hyperbole so even if he said it we don't know if it would be true. But the quote in itself comes from the point of the manpower capabilities of the Revolutionary Republic which before that was unseen. The closest would be the Abassids fighting the Tang in Tibet.maybe a thousand years ago? If we can trust those numbers?
(The mongols I don't dare to say because the numbers given by Western/Muslim account is staggering and could very likely be multiple reports of same army but just moving fast enough that it "appears" in two places)