One thing to note about comparing Han with Rome is that the Roman Empire under the principate was the most advanced western state before modern times. Today we are accustumed to think that technology and living standards always improve with time, but that's not true. 1st century Roman technology and living standards were only surpassed in the west by the 19th century, according to modern archaeological data and theoretical research. So if Han China was more advanced than the Roman Empire, so later dynasties such as Song and Ming were even more advanced, so China was hugely more advanced than Europe for 1800 years of the last 2000 years. I think that's too much of a stretch.
I guess that China was more advanced than the West (which refers to Europe, North Africa and Western Asia, which includes syria, judea and asia minor) from 400 CE to 1400 CE. A period of 1 thousand years.
I have made this graph illustrating the rise and fall of classical civilization and the long term trend of China and the West. Both show a tendency for advancement over the very long term, but with huge discontinuities and in the case of the west, a 2,000 year long cycle:

The rise of the ancient west was a very fast and dramatic process in long run historical terms. This is revelead in the following archaeological data:
1 - Size of the houses. Houses escavated in the 9-8th centuries BCE in Italy and Greece are very small and very simple hut like structures. By the 1st century CE the typical Roman house was larger than the modern American house (though the number of inhabitants per house in Roman times was much greater so the per capita housing space was smaller, but it's large, probably around 400-500 square feet per capita). Per capita housing space increased about 10 fold in Italy and Greece from 800 BCE to 1 CE.
2 - Quality of the houses and the number of things found inside the houses. Houses in the 8-9th centuries BCE were made of simple materials such as wood and dirt. Houses of the 1st century were typicaly made of brick, mortar and plaster. The number of metal utensils found in Graeco-Roman houses also increased hugely, Ian Morris guess a probable 10 times increase in per capita supply of utensils, furniture and other household stuff.
A hut, typical residence of pre-classical peoples and the tribes around the empire:

Remains of a wall in Pompeii:

Clearly there was a huge difference in living standards between Pompeii and the tribes around the Roman Empire. Pompeii was build with almost modern technology while celtic villages were made of pieces of wood and stone found in the forest. The average pompeian had 10-15 times the housing space of the average celtic village dweller. It is untrue to claim that living standards were similar in all pre-industrial societies.
The decline and fall of the Roman Empire was not just the decline and fall of an empire, but it was the collapse of an entire civilization. By the year 700, almost nothing remained of civilized living standards in Europe, Western Asia and North Africa. Some regions such as Syria and Egypt held out better than others and still preserved some rudiments of civilization but the overall picture was terrible. This is reflected in the archaeological remains, we have much more buildings and shipwrecks and levels of lead and copper pollution from the early roman times as compared to the early middle ages. The shipwreck data is the most impressive:

It is also strongly correlated with other indicators, from levels of lead pollution in Greeland ice cores to the number of dated building inscriptions.
The shipwreck data also underestimates the rise and fall of long distance trade during ancient and medieval times. Roman ships were several times larger and safer than medieval ships, so they tended to get wrecked less often. It is like measuring the size of the US car fleet by counting car accidents, today the US car fleet is over 20 times larger than it was in 1920, but the number of car accident related deaths didn't increase by 20 times, as cars got safer.
Roman sea trade was in the order of several millions of tons. Only equalled in very recent times, for comparison Longon in 1800 CE moved 800,000 tons of cargo, while Rome imported 400,000 tons of wheat alone in the 1st century, Rome's 1st century port probably moved a larger volume of cargo than London's in 1800 CE.
For China my graph shows a gradual rise for nearly 2,000 years, with minor declines such as the fall of Han, since we don't have anything like what happened in the fall of the roman empire for sinitic civilization. The mongol invasions created a decline, but it was reverted and the level of civilization in 14th century China wasn't much worse off as compared to the 11th century. Chinese levels of metal production show such rise and levels of per capita iron production during the Song were higher than during the early 19th century. So I put the Song as the zenith of pre-modern Chinese social complexity.
Edited by Guaporense, 24 July 2011 - 06:10 PM.