Back on topic, I've read around a little more and something I found surprising was that the late Han army had a system of conscription in which common soldiers spent as much time in training as they did in combat- even common infantrymen were given a year of training, which is roughly double what a modern rifleman would go through. A full-time paid army was maintained near the capitol while the conscripts held the borders, and in a crisis they could call up the militias, which were full of men who had previously undergone a year's worth of training as conscripts. Most of the population in the early Han were yeomen farmers, not serfs or slaves. So with all these factors combined we can expect Han armies, even the militias, to be relatively effective and disciplined. They also had a tons of crossbows.
So, I'd previously thought the Han infantry wouldn't be much of a concern for a legion, but now I'm thinking it would be much more dangerous. I think the tide of battle would basically come down to the maneuvering before engagement- if the Romans could pin the Han army down they would probably be able to hack their way through and score a major victory. If the Chinese had the choice of battlefield, we'd probably see the legions bloodied by crossbow fire while their cavalry was broken, left unsupported against a more mobile enemy with greater firepower.