Who would win in a hypothetical war: Han China or the Roman Empire?

This war would revolve around four main factors-

1. Terrain and supply- where are you fighting this war?

2. How much Calvary are we talking about? The key factor for both armies.

3. Populations and ability to commit sustained resources- who could best sustain a long-term war of attrition of this magnitude.

4. Would be- what are the goals? territorial expanse, dominance of trade, religious? Motivation for conflict and zeal to fight and win.

Need more details- GO!

Which period of the Roman Empire?

I'd probably say the Romans, given their effectiveness.

Both at their heights

We try but we didn't have long
We try but we don't belong...

-Hot Chip (Boy from School)

Well you can't just say fight a war ;)

To invade a country that has a strong military is far more difficult then to defend against an invader with one.

The population of the Han empire was registered as having 57,671,400 individuals in 2 A.D.

At it's peak, about the 1st century A.D.- the Roman empire had a population of about 60-70 million.

To invade and enter China from the west is far more difficult (mountainous, endless steppe and desert, which has been China's natural barrier and protection since the beginning of it's culture, only allowing for nomadic Mongol invasions) then to enter the Roman provinces through Russia or Persia where there is ready access to fortified cities and cultivated resources to launch an attack from- to stable horses and supply the invading army.

I think that tactics would be a small part of the equation and terrain everything, so the Han have every advantage for an invading force.

If we look at the success of the Hun invasion of Europe with the united might of the Roman empire and Germanic Tribes opposing them, then we can get a picture of what a Han invasion would look like. For the Huns, the use of the horse was the deciding factor in their success and the Han Empire was also known for the strength of it's calvary. The Romans mostly depended on Germanic tribes for their calvary and the numbers were probably far lower as the legionnaire was the main fighting element of the Roman war machine.