In a direct conflict I would say the Romans would have won.
Here is the reasoning for why I think this is the case and as you may know this is only my opinion and I am open to other opinions.
The Chinese fighting prowess can be measured against their cousins the far east Turkics who are world class and peak military element.
The chinese armies like Han and Tang have managed to beat the nomadics twice and the reason for that is because the turkic nomadics lacked one thing China never lacked which is civilization and governance. The Nomadics were divided people and had rough culture with infighting tribalism embedded meaning they were always fighting amongst each other and settled in tribal divisions hence it was easy for the civilized Chinese to defeat them in their weaker divided eras.
But however whenever they united they overran China effortlessly and not only china but half of the known world. The turkic steppe and Mongols are traditionally best soldiers on earth and the Mamlukis slave soldiers were purchased by every single sultan in the middle ages as his personal guard because they were famous and praised combatants.
Genghis overran China and his grandson ethablished Yuan dynasty And another nomads have overrun China the Qing dynasty aka the Manchu.
China managed to defeat the Turkics steppe nomads twice and the Turkic/Mongol/Manchu overrun China twice.
China managed to even chase some turkics during the Tang dynasty to Europe.
The Chinese could have only defeated the Steppe people during periods of civil strife and great division and the steppe people were less organized nomads who rarely came together but when ever they did they defeated China.
But these steppes didn't only defeat China because they defeated the Iranians, Arabs, Romans, North Europeans such as Germans, Russians and everyone else under the sun. Hence China being defeated by the steppe folks twice is nothing negative.
If I have to rate ancient chinese Empires in military prowess I would say Han Dynasty and Tang Dynasty were both at the same level and equal to the Sassinds and Byzantine but not the original Roman empire because that empire was stronger in comparison to Han or Tang including Byzantine or the Sassinds..
There is 5 class of empires
1: Small empire: Kingdom of Denmark, Joseon Dynasty of Korea, Moldova, Dracula's kingdom, Hittites,
2: Average to small empire: Hungarian empire, Serbian empire, Malacca Sultanate, Sparta and Athens, Samanids, Prussia kingdom, Germanic empire.
3. Middling empire: Song Dynasty, Safavids, Austrian-hungarian empire, Spanish empire, Seljuqs, Khwarazmian Empire, Ghaznavids, Ming Dynasty, Qing Dynasty, Golden Horde, Ghurids, Ilkhanate, Yuan Dynasty, Achaemenid Empire, Neo-Babylonian Empire. Kievan Rus'
4. Big sized Empire: Tang Dynasty, The Sassinds, Byzantine, Moghul Empire, Ayyubid dynasty, Han Dynasty, Delhi Sultanate, Assyrian dynasty, Timor the Lane's Timurid, Macedonian empire (Alexander the Great) Al-Andalus, Isabella and Fernandez of Spain, Al-Mamluki sultanate of Egypt, Portuguese empire, Napoleonic dynasty and Russian empire.
5. Gigantic sized Empire: Ancient Egypt, The Caliphate (Ummayyid and Abbasid) Roman Empire, Ottoman empire, Mongol empire, British empire, Currently USA..
There has been 7 transnational empires on large scale until currently if you include the United states of America because imo they are a dynastic era element