This is a very interesting question. Thanks for asking it. I'm always interested in figuring out what historical peoples thought about each other, themselves, their place in the world, art, medicine... Intellectual histoyr is infinitely fascinating, but difficult to delve into. Regarding my credentials: I'm a law student with a BA in history. I took a seminar on early modern japan two years ago. I am not an expert in this field.
First, some sources from people who are/were expert (or otherwise useful sources):
"The disputes among European observers (i.e. ten Kate and von Balz) as to the nature and significance of the intellectual and emotive characteristics of the Japanese, were reflect also in the earlier estimates of their physical constitution. Their small stature, for the most part, and a certain frailty inferred therefrom, led members of the white race to discount their future as, in all probability, of little or no consequence in the future achievements of mankind." ^1 Notably, they regarded the Japanese as the "head of the Mongols" intellectually, but not physically.
The works of Engelbert Kaempfer, a Briton who wrote about his experiences in Japan in the 18th century, would have substantially shaped Western perceptions. Elizabeth Wallace argues that Kaempfer often "not only suggests the dire consequences of Japanese isolationism, but also articulates a personal resentment over the circumstances isolating him from the country he so desires to know." Though Kaempfer was frustrated with his difficult position at Deshima (basically an isolated prison-island for Dutch traders to work out of), he wrote about a ton of stuff: reptiles and insects, fish and shells, medical practices, the political state, religious practices, detailed accounts of cities from palaces to brothels... the list goes on. ^2
Rotem Kowner argues that in the 19th century, "Westerners had only a vague idea concerning secluded Japan and the racial constitution of its people... In the first few decades after the American squadron under the command of Commodore Perry ended two centuries of Japanese self-seclusion, the West was faced with a bulk of novel information about the rediscovered archipelago and its people." He recounts an excellent quote from a westerner in 1876: "We have been accustomed to regard that country as uncivilized, or half-civilized at the best, but we found here abundant evidence that it outshines the most cultivated nations of Europe in arts which are their pride and glory, and which are regarded as among the proudest tokens of their high civilization." Kowner also argues that in initial Western contacts with the Japanese, European visitors had "no technological advantage over the Japanese." ^3
Now here's my 2 cents. Modern Japanese scholars have rejected the old view that Japan was totally excluded during the Tokugawa era. Historians recognize that though the premise of sakoku is basically true, there are lots of exceptions: Portuguese missionaries, Russian diplomats, German/Dutch/English traders, and plenty of contact with other Asian countries. These are exceptions, however. Lots of Westerners just didn't know a lot about Japan. The sources do seem to indicate that racial and imperial classifications of Asians, coupled with Western technological dominance, would have tinged Western perceptions of Japan.
Frankly, most people probably didn't know much about Japan at all. The ones who did might have read the (relatively few) personal accounts of Westerners who had traveled to Japan. Those accounts would probably dispel the idea that Japan was some incredibly backwards or "savage" country (as defined by Westerners in the 19th century). However, by the 19th century, Westerners undoubtedly thought of themselves as more technologically advanced and of a superior racial stock. I think the above quote (uncivilized or half-civilized) hits the nail on the head.
^1 The Japanese Race, Alexander Francis Chamberlain The Journal of Race Development, Vol. 3, No. 2 (Oct., 1912), pp. 176-187
^2 The First Samurai: Isolationism in Englebert Kaempfer's 1727 "History of Japan" Elizabeth Kowaleski Wallace The Eighteenth Century, Vol. 48, No. 2 (SUMMER 2007), pp. 111-124
^3 'Lighter than Yellow, but not Enough': Western Discourse on the Japanese 'Race', 1854-1904 Rotem Kowner The Historical Journal, Vol. 43, No. 1 (Mar., 2000), pp. 103-131
Nellie Bly in her journey around the world in 1889 stayed in Japan for a few days, and while her opinions are more of an uneducated tourist than any kind of expert, she's a pretty good representation of what an average woman on the street might have thought about Japan. It does a good job of demonstrating both the ethnocentric western disdain for Asia, while also showing the fascination with Japan that was so popular during the time. The whole book is available at the link, and as usual for Bly it's really fun reading.
If I loved and married, I would say to my mate: "Come, I know where Eden is," and like Edwin Arnold, desert the land of my birth for Japan, the land of love–beauty–poetry–cleanliness. I somehow always connected Japan and its people with China and its people, believing the one no improvement on the other. I could not have made a greater mistake. Japan is beautiful. Its women are charmingly sweet. I know little about the men except that they do not go far as we judge manly beauty, being undersized, dark, and far from prepossessing. They have the reputation of being extremely clever, so I do not speak of them as a whole, only of those I came in contact with. I saw one, a giant in frame, a god in features; but he was a public wrestler.
The Japanese are the direct opposite to the Chinese. The Japanese are the cleanliest people on earth, the Chinese are the filthiest; the Japanese are always happy and cheerful, the Chinese are always grumpy and morose; the Japanese are the most graceful of people, the Chinese the most awkward; the Japanese have few vices, the Chinese have all the vices in the world; in short, the Japanese are the most delightful of people, the Chinese the most disagreeable.
[...]
The Japanese are very progressive people. They cling to their religion and their modes of life, which in many ways are superior to ours, but they readily adopt any trade or habit that is an improvement upon their own. Finding the European male attire more serviceable than their native dress for some trades they promptly adopted it. The women tested the European dress, and finding it barbarously uncomfortable and inartistic went back to their exquisite kimonos, retaining the use of European underwear, which they found more healthful and comfortable than the utter absence of it, to which they had been accustomed. The best proof of the comfort of kimonos lies in the fact that the European residents have adopted them entirely for indoor wear. Only their long subjection to fashion prevents their wearing them in public. Japanese patriotism should serve as a model for us careless Americans. No foreigner can go to Japan and monopolize a trade. It is true that a little while ago they were totally ignorant of modern conveniences. They knew nothing of railroads, or street cars, or engines, or electric lighting. They were too clever though to waste their wits in efforts to rediscover inventions known to other nations, but they had to have them. Straightway they sent to other countries for men who understood the secret of such things, and at fabulous prices and under contracts of three, five and occasionally ten years duration, brought them to their land. They were set to work, the work they had been hired to do, and with them toiled steadily and watchfully the cleverest of Japanese. When the contract is up it is no longer necessary to fill the coffers of a foreigner. The employé was released, and their own man, fully qualified for the work, stepped into the position. And so in this way they command all business in their country.
Follow-up questions:
When you say "people seem to think that ..." do you mean Japanese people?
Are post-Meiji Japanese depictions of 1200's Japan and 1600's Japan different or the same? (If they're different, that seems to imply that post-Meiji Japanese do recognize a difference between "middle ages" feudal Japan and Edo "nation state(?)" Japan.)
Do you have an example of such a depiction? I'm not sure I understand your question properly.
Wojiz and SadDoctor offered some good accounts. I just want to add something.
This is what MacArthur said at Japan's surrender in WWII:
We stand in Tokyo today reminiscent of our countryman, Commodore Perry, ninety-two years ago. His purpose was to bring to Japan an era of enlightenment and progress, by lifting the veil of isolation to the friendship, trade, and commerce of the world. But alas the knowledge thereby gained of western science was forged into an instrument of oppression and human enslavement. Freedom of expression, freedom of action, even freedom of thought were denied through appeal to superstition, and through the application of force. We are committed by the Potsdam Declaration of principles to see that the Japanese people are liberated from this condition of slavery. It is my purpose to implement this commitment just as rapidly as the armed forces are demobilized and other essential steps taken to neutralize the war potential.
The energy of the Japanese race, if properly directed, will enable expansion vertically rather than horizontally. If the talents of the race are turned into constructive channels, the county can lift itself from its present deplorable state into a position of dignity.
I'm still not sure what you're asking but:
If you're asking if Westerners thought 19th Century Edo Japan was "feudal" and technologically backwards, the answer is well, Yes. Because that's the reality. The Shogunate knew that, and once they actually fought, so did the Sonnou Joui faction. The entire Bakumatsu and early Meiji was basically Japan trying to strengthen internally so they can respond properly to external pressures.
But for cultural and art, as pointed out, visitors to Japan held them in incredibly high regards, even before the Meiji. People like Thomas Glover liked Japan so much they went very native and helped the Restoration a lot. And of course once the Restoration went underway, Japan kept impressing Western visitors about just how far and how fast they were learning and adapting western ways. And of course, Japanese culture kept impressing Western visitors.