Hmnnn,imaginary wars,these arguments can go on....and on...and on - and really nobody knows because we have no ( sensible ) context to put it in
Lots of fun though, so I think I'll have a go myself
If we're talking about both empires at their peak I think its hard to call because both were pretty much invunerable.
We could argue about the old chestnut of Western armour versus Eastern mobility far ever but these things decided battles, not wars. For every Mongol horde surrounding closely packed European Knights or Eastern horsemen swamping isolated Roman Legions, you have a Macedonian phalynx smashing through Persian front lines or a Frankish shield wall
rolling over Saracen horsemen.
It was the machinery behind the individual armies who decided wars ( and still do ) - determining who was beter equipped, organised, supplied etc.
Both these Empires were seriously well organised and barring and early, cataclysmic defeat for either side ( almost unthinkable given both sides resourses ) whichever side was on the back foot would be able to roll with the punches and learn how to fight their new enemy.
Romes probable superiority in the field would not be enough for complete victory as the never ending struggle of the Roman/Byzantine Empire versus that of the Persians/Parthians shows - the Romans were usually on top but never really conquered them, that took the Islamic armies who took advantage of the two worn out behemoths after their final epic confrontation and conquered most of both empires.
The Romans famously relentless approach to war would not have been decisive either - the Great wall alone is enough to show that the Chinese can match anyone for sheer bloody mindedness.
The obvious advantage for the Han would be sheer weight of numbers, but this wouldn't be sufficient either.
The Romans true military talent wasn't tactics or technology
( although advanced in both ) it was the ability to raise armies.
The Romans lost almost as many battles as they won, but unlike anyone else Rome could absorb huge military disasters without breaking a sweat. We hear of them losing an entire army of 50,000 in a day, but before their opponents had finished celebrating their victory they could see another Roman army on the horizon -of identical size, identically trained and identically equipped as the last - but they knew about the last battle and had learned from it - it was like fighting the Borg. Basically, the Romans are built for wars of attrition and you will never wear them down.
Someone made the point that Chinese are better warriors, hardly, its obvious from history that all peoples are capable of fighting like lions or running like cowards, it depends on their attitude at a particular time - unshakeable religious belief or confidence in your commanders help, infectious defeatism or lack of supplies obviously don't.
If its the late Han Empire the Romans would conquer the individual fractured areas one by one
By the same token if its the late Roman empire the Han would swamp them a la the Barbarians
Finally then,who'd win?
I think after the first few bloody and inconclusive battles they would learn to leave each other well alone and go pick on some "savages" instead. Maybe some sort of cold war as befitting two superpowers. Or Rome would win on points. Or something.....ok, I still havent a clue.