Tomes could be written predicting the outcome of such a battle. Myriad details and circumstances could yield triumph, or humiliation for either side. Where does the battle go down? What are the troop strengths? Full Armies? Who commands either side? How would the terrain effect the outcome?
I am not an expert on military history, or ancient civilizations, but I nonetheless enjoy wondering about such things. Han China Vs. Republican Rome or we could roughly say Western Han Vs. Republican Rome and Eastern Han vs. Imperial Rome.
The way I see it, they would probably have to meet somewhere in central Asia - Western Afghanistan or Northern Persia (Iran) in order to both be equidistant from their respective capitals. I would put the Chinese forces at roughly 1.5-2 Million men, and Roman Forces at anywhere between 500,000 and 800,000.
It is a tough call. Obviously China wins the numbers game hands down. Also their missile technology was marginally superior, so we can give them superior archers, though they lacked onagers. China also wins with cavalry, both in numbers and horsemanship. That leaves infantry. Chinese peasants Vs. Roman professionals. This is an enormous advantage for the Romans. Rather than tainting the discussion with my own predictions, I invite you to say who would win, why, and under what circumstances would the victory be reversed.
I hope my nom de plume does not betray my allegiance!