Smithnikov said:
Warring States era Japan (united, under Nobunaga) vs. The Roman Empire (under Julius Ceasar)
My money is actually on Nobunaga.
By the time of Nobunaga, Japanese armies were distinctly early modern in character, with pike and shot being predominant. While the Romans had faced Greek pikemen, early modern pike armies were a very different story and were basically unbeatable even in their own time period. Additionally, where the Romans really had the edge on their rivals was in logistics and organisation, but against an early modern army they don't even really have that advantage.
You might think that the Romans would be able to field enormous numbers to compensate, but when you look at individual battles Roman armies really aren't bigger than those which fought major battles in Nobunaga's Japan. For all its vast conquests, Rome under Ceasar is still essentially administered like a city-state. The proportion of the population who is even eligible to join the army, let alone willing to do so, is actually very small.
So yeah, Nobunaga wins.
Anyway, err..
Dumbledore versus the Balrog.
Better than Gandalf? Worse? About the same?