Global Politics in the 21st Century, by Robert J. Jackson, repeats the claim that European ships were "drastically inferior to Chinese ships in every respect imaginable even as late as 1800". This seems to be quite a claim.
Moreover, its reference for this is a book called The Genius of China, which doesn't exactly encourage confidence.
China isn't exactly famous for being a naval power, either. I know for certain that at one point they had that exploring / treasure fleet, but aside from that? To say that China's ships were superior in every aspect at the start of the 19th century is just... huh?
In the 18th century, Europe had 200-gun ships-of-the-line, and I've never heard of China having anything even remotely similar.
Please tell me my textbook isn't a complete waste of money.
The Chinese explorer Daxi Hongtong reportedly reached the Arabian peninsula in 674 AD. It wasn't until the Viking Age a few centuries later that Europeans could claim similar range. The great admiral Zheng He (1371–1433) explored the coastlines of Asia in ships larger than that of Columbus and made it as far as Mombasa and Mecca. Zheng He's flagship was about 67 meters long. By comparison, Henry V of England's flagship, Grace Dieu, commissioned in 1420, the largest in Europe, was about 66m long. These were both exceptionally large ships for their age, but I think it's safe to say that the Europeans caught up with the Chinese sometime during the 15th century. In 1522 Magellan's fleet circumvented the Earth. By 1800, European ships were far superior and this is a major reason why Europeans went on to dominate Asia and "humiliate" China for 100 years.
One innovation that Europeans did copy from the Chinese in the early 19th century was watertight compartments. European ships were apparently superior in every other respect.
The height of Chinese naval technology and power was in the early 15th century, but after the Ming Emperor Zhu Di, none of his successors saw need in developing the navy anymore. Well, that was partially the problem. The other part to the problem was corruption, or gross inefficiency when it comes to the navy. "The Empire's troops [did] not take care of the ships", as the famous Ming general Yu Dayou (1503 - 1579) has put it. He observed that "the Empire [spent] lots of money on building the ships, but none [was] of usable quality", and that "most ships, after its construction for about a year, would be sunken and no longer be used". His advice was actually "[he would] rather have the ships built by the people than have it built by the Empire".
Source: China's Research On the History of Ming in the 20th Century (20 shi ji zhong guo de ming shi yan jiu).
Caveat lector, I am in no way an expert on Chinese ships or shipbuilding, but I may be able to provide an answer on European ships and how they changed over time. Something to keep in mind is that there are a ton of fables that center around the admiral Zheng He, who seems to have bene a real person who existed and led several voyages of discovery, but whose achievements and the size of whose ships is substantially exaggerated. For example, this image tends to circulate on the Internet when Chinese treasure fleets come up; it purports to compare one of Zheng He's ships to one of Columbus's ships, but the purported Chinese treasure ship would literally be impossible to sail, even if you could build it; the notion of having off-center masts is laughable and a wooden ship that size would hog, sag or twist itself apart in any sort of a seaway.
On the flip side, it's also worth pointing out that no such thing as a "200-gun" ship of the line ever existed; the largest of the age of sail was the Nuestra Señora de la Santísima Trinidad, built to carry 112 but eventually enclosing a fourth gun deck to have a total of 140 guns.
So to get to the crux of your question, were Chinese ships "better" than European ships at the start of the 19th century? Well, is an apple better than an orange? What I know about the sea-going warships that were being built in China at that time is that they were meant for coastal patrols and as anti-piracy vessels, and also ships that could navigate up the large rivers into China's interior. Chinese trading ships were meant to be able to reach into its extensive trading empire extending to the Indonesian archipelago to the south, the Japanese islands to the north, and India to the west. I don't know the extent to which the Chinese state had a navy to patrol those sea routes or provide convoy or other systems of protecting trade, but that would be a good starting point.
Anyhow, attached are some comments I've written and/or threads I've been involved with regarding Western ship design, hopefully this can be helpful to you. If you have follow up questions, please ask!
https://www.reddit.com/r/AskHistorians/comments/2709jm/how_would_a_britishhms_frigate_built_in_1715/
https://www.reddit.com/r/AskHistorians/comments/2fs8qr/how_much_more_advanced_was_a_british/ckcdgbf
https://www.reddit.com/r/AskHistorians/comments/3pn7v5/what_changes_occurred_in_the_construction/
