i understand that u think that Rome was the greatest empire in the ancient times. that's because of ur education and the global trend. right now the western world basically dominates earth, therefore it's understandable that people think the western world has always been the most advanced sector of the world since the begining of human civilization, thus Roman empire has AUTOMATICALLY BECAME the most powerful empire in the ancient era. however, what the absolute majority of westerners don't know (no offence here and i'm not boasting AT ALL) is that China was the most advanced country of the world until about early Qin dynasty(about 1700) and occupied over half of the world's GDP until about mid Qin dynasty(about 1800). i.e. China was the richest and most advanced country for an absolute majority of its 5000 year history(it only started to fall at the begining of the modern age.
when we talk about comparing the Roman empire and Han China, well, based on fact, Han's technology and economic capability far outweighs Rome(e.g. a Han peasant was actually owning more wealth than a Roman aristocrat)-no offence again. in term of battle capability, Han holds the absolute technological advantage again(e.g. full body heavy armours that can not be penetrated by spears are given to every soldier, mass production of swards at one time instead of manufacture one by one). Han also holds a numerical advantage. however, in the agricultural era, anything is possible in a war (leisurely armed peasants can overthrow a government much easeir than they would now). for example, the 'slave army' led by the famous Spaticus(correct me if i've spelt it wrong) has caused great trouble for the Roman empire. same in Han, the fact they we've got so many dynasties in our history is self-explanatory. However, i would still say Han could defeat Roman easily. i think most of u know that Han defeated the Huns in the Wudi era. however, i'm sure that not most of u don't know some of the remnants of the Huns after they had been defeated, had escaped west to Europe and had some battle with the Roman army, and they actually won these battles. According to this, Han should defeat Rome easily at the time. one more thing i have to say is that Han dynasty wasn't the 'peak' time in China's ancient history. our 'peak time' is the Tang dynasty which was established sometime after the end of the three kingdome era (three kingdome era is right after the fall of the Han dynasty). i'm not an expert in history and if u want to check out more Chinese history, search the web and i'm sure u would find tons more than what u think our history is all about.