What did the Han created that was more advanced than what was being produced in Rome?
This is an interesting question and not easy to answer, because of historial issues. Anytime you deal with ancient societies, things get tricky. Here are few things that the Chinese built around this time:
1. Part of the great wall of China.
2. Some military innovations such as the battering ram.
3. Some say the compass.
4. Mandarin Chinese language,
5. Mini hot air balloons.
Now the question is whether these were more impressive than what the Romans built. If I had to take a guess, I would say that the only two things that the Chinese made that probably exceeded the Romans are: (1) The Great Wall of China (probably more impressive than Hadrian's Wall. (2) Mandarin Language.
In the end, they were both great civilizations.