Hi SkyOdin!
I only know a little about the cultural development of Japan and China but in terms of an increase in raw technological level, there wasn't a vast increase over this period that I am aware of.
I am not talking about art and culture; I am talking about technology and science. Were the Samurai not still using muskets before Perry arrived, of the sort europe had stopped using several centuries before or is this also a myth? Was it not a fact that Perry had a steam powered ironclad squadron to intimidate the Japanese wooden sailing ships, just as we had done a few years earlier to the Chinese. These are facts, as far as I aware (unless Perry himself was lying; this impression comes from his own account that was published after his return to the US). When you consider that Chinese culture was so far ahead of the west in science and technology in the early medieval period, this equates IMHO to an empirical phase of relative technological stagnation in these two nations, when compared to the West, over this time period.
First off, there are plenty of historical sources other than Commodore Perry's from the time. It is not like the Japanese didn't have a written language.
Here is the funny thing though, you are using the example of the steam engine as the prominent example of the more advanced technology of Europe. But here is the thing, the development of the steam engine was a fluke of history. Steam technology has existed in Europe since the scholars of ancient Alexandria devised steam engines as toys and amusements. The principles are so basic that most major civilizations, including the Chinese, understood them. The trick is that steam engines are horrifically inefficient unless until they reach a certain level of sophistication. Most civilizations had no reason to pursue steam technology to the point where it became viable.
Steam technology developed in England as the result of an unusual confluence of geography. Before you can have steam engines, you need coal. The only culture that can develop steam technology is one that is mining coal. This is because the environment of the coal mine itself is the only place where undeveloped steam technology can be refined, since a nearly unlimited amount of cheap, readily available fuel made up for the inefficiencies of early steam engines. In England, early prototype steam engines were used to drain water out of coal mines. Over time, these inefficient engines were refined into the more efficient ones that became the back-bone of the industrial revolution.
Now then, similar circumstances to the ones that occurred in England did occur elsewhere in the world at another time: in 12th century Song dynasty China. In the north of China are massive coal deposits, and the Song dynasty Chinese were taping into those deposits in the 12th century to fuel their massive steel industry. At the time, China was producing an amount of steel that would not be seen until the Industrial Revolution. There was only one difference between 12th China and 18th century England: the coal mines in China were dry. There was no need to pump water out of them using big, inefficient steam engines. That one difference may be the reason why China didn't industrialize in the 12th century.
The steam engine is not an inevitable result of some abstract notion of progress. It is something that resulted from very specific conditions. It is like asking why the Incans didn't have the wheel, even though they had a sophisticated road infrastructure. The answer is simple: they lived on steep mountains. Wheels were pretty much useless. As the saying goes: "Necessity is the mother of invention". The reason that Japan was still using a 200 year old musket when Commodore Perry arrived is because they hadn't fought a war in 200 years.
The real test of civilization is in how it adapts to a changing world. In that regard, Japan succeeds admirably. In a few decades, Japan went from a country 200 years behind Europe technologically to the country that completely stomped Russia in a naval battle. The real big question is how China, the most advanced civilization on Earth throughout history up to that point, failed to modernize. Greater historians that I have tackled that question and failed, but I do have some theories. Most notably, China is a big, populous country. It simply takes more time for a big country to modernize and build up infrastructure, and it got overrun by foreign powers and torn apart by internal dissent before that could happen.