Alright, I'll bite. Let's set aside the Greeks and just look at (Imperial) Rome and the Han.
Now I'm not going to lie, my opinion of the Han empire is low. The Qin dynasty knew their shit better, the Han eventually fucked up hard enough that they lost their country to rebels.
Let's say, though, that we assume roughly equal size (a legion versus an army of no more than 6000 men) and a central asian battlefield.
My first instinct is to just hand it to the Romans and walk away. They've got better heavy infantry, and both sides fielded cavalry in small proportions to their infantry, usually surrounding officers. However, there are a couple of turning points.
First, if anybody is going to challenge the Romans in siege engines, it's going to be the Chinese. I'm not saying its a sure thing, but they're the only ones out there with comparable tech. Also, there is a really dramatic difference in cavalry quality there, even if we assume the Romans have just brought along Armenian Auxiliaries or somesuch. The Chinese will have stronger horse, while the Romans will have superior foot. Archers won't make much of a difference on either side, because the Chinese are unaccustomed to heavy armor fielded on that scale, and the Romans think arrows are for fags.
...Yeah, Rome. Unless the Chinese general is noticeably superior, and launches a fire trap or some other manner of stratagem, Rome has my confidence. My real question is how the Han managed to get their army all the way out here.