if you look at China's empire as a whole, with highlights upon the Tang dynasty and the Han dynasty, I would say the Chinese empire is relatively the "greatest".
I tip my hat to the power of the Roman empire, but there are very few things things that the Romans had that the Chinese didn't have and more.
Also, the very fact that the entity of the Roman empire does not exist and the Chinese entity empire does to this day. Imperial China has 5,000 years of history, and the Chinese civilization has existed for even longer. Namely the Shang dynasty that has records from 12,000 B.C.
Unlike the Roman Empire, the Chinese Empire can say that there was a point in their history when the entire wealth of the rest of the world was incomparable to the wealth of China.
China's trade, in the Tang dynasty especially, was monumental. Silk was equivalent to gold, and was created in pre-history China.
When the near invincible Mongol army began conquering Eastern Europe, the Middle East, and China, it took the longest to conquer China (40-50 years); however, it took a minimal amount of time to conquer Rome (but I recognize the fact that Rome was already on its decline).
The Chinese cultural has deeper roots than any other culture, not saying this out of bias, but just out of historical evidence and historical time. The Chinese cultural has so far been impossible to bring down, despite the rule of foreigners for two times. And for each time (Mongols and Manchurians), the foreigners failed to defeat the entity of China, and many would say that they became "chinese themselves".
China's main historical issue was that it had too many civil wars. Every time there would be even a 30 year peace, the economy of China would sky-rocket. Despite a history of internal strife, China still retains a constent identity even while rulers are being replaced, foreigners are taking over, etc.
The Roman empire was never truly unified under one standard. Ever since the Qin empire, all the standards, namely language, has been united.
It can be said that the Roman empire's unity was largely due to its military. In the Chinese empire, it did take many wars to unite China after another separation, China remained unified by culture.
Yes, the Romans had domination over the Mediterranean, but their ships were incomparable to the Chinese ships (especially in the Ming dynasty).
Where the Romans can be seen as "greater" is in their desire to conquer other lands. China for the longest period in history had the greatest potential to take over much of the world(with its population, cultural identity, nationalism, and advancement); howevever, China never really had an interest in imperialism--unlike the British and others.
Unlike Rome, China has always "existed", and Rome can be said to have been "created" and then "disappeared."
I think a sad reality is that much of the world that is eurocentric view China as the image it had during European imperialism. At the time, China was being ruled by Manchurians who had hindered China's economy drastically by limiting trade. The Manchu empress was uneducated and beheaded any advisor that believed that China had to change ("people who were once barbarians and lesser are now able to defeat us"--one advisor). This quote is quite racist, i know, but it refers to the view of China on the Japanese--who's culture was learned from China.
Imperialism, Japanese invasions, rise of Communism, weakeness of the Manchu government were all factors that contributed to the later humiliation of the Han people of china.
Modern-day western views generally take from the lowest point in Chinese history.
I know it's hard to win my argument with a bunch of fluffy comments. But here's a self-test if you doubt my opinion:
Take any time in European history (I'm serious. Any time.)- preferably before the Imperialistic Era in Europe. You'll find that during any time in European history, the Chinese empire was alive and strong. And if you think that it is only because China had a minimal amount of competition, look at the Mongols, as I earlier stated: Mongolians who basically had no standing army but an army on horseback, easily took over eastern Europe and the Middle East, while taking the longest to take over China. This is also the reason why China experienced the greatest brutality from Mongolia, when the Mongolians went into China, they found it to be...well too populated, and literally began to lower the population by execution. I mean really, what other nation that has experienced mass genocide could still continue to hold rebellions and revolutions, and eventually become a world power again?
But anyways, I can say that I definitely know more about European history than Chinese history; but it doesn't take a lot to realize the great extent of the Chinese empire.