I'd recommend R.F. Tylecote's A History of Metallurgy. I don't know what he says about the period in question, but he did write the textbook on the subject you're interested in.

I thought about writing a long post about how you should go into a subject to try to understand it and not just to prove a preconceived notion. I think this is especially true of metallurgy and military technology where a lot of people want to talk about what was "better" and more "advanced." They fail to see the variability that existed, how culture shaped the way that technologies developed and were used, and that benefits in one aspect usually mean drawbacks in another. Oftentimes, different technologies aren't better or worse, they're just different.

It may be fun to argue "knight versus samurai" in some thread. But if you actually want to learn more about metallurgy, it would help if you go into it with an open mind and trying to understand why different people came up with different ways to do similar things.

I know a bit about the history of bronze. Copper is not a particularly strong metal, and its relatively high melting point makes it difficult to cast. Cyprus was an early producer of copper and a supplier of Egypt and Greece, and certain mines in Cyprus were found to have particularly quality ore. This is because the ore also contained arsenic, which can be alloyed with copper to make bronze to form a metal with better strength and lower boiling point. By 3000 BCE the Egyptians' bronzes were almost exclusively arsenical bronzes.

However, an even better secondary metal was soon found: tin. Tin bronzes had the advantages of being even stronger than arsenical bronzes without the toxicity of arsenic fumes produced by smelting. Tin bronze, then, gradually supplanted arsenical bronze as the prevalent alloy of the Mediterranean.

There's a very good overview here:

http://mygeologypage.ucdavis.edu/cowen/~gel115/115ch4.html

I can talk about metallurgy in the ancient world, and I think it will surprise you.

Basic info for anyone reading this without metallurgic knowledge. There are two categories of worked iron: wrought iron and cast iron. They have different carbon contents, and the carbon content of steel (a superior alloy) is between the two. Production of wrought iron involved softening and working metal extracting from ores, while cast iron involves melting the metal entirely and casting it.

The Iron age started around 1200BC, but different civilizations worked iron and steel in very different ways. In China iron was cast from an extremely early date, certainly from the 4th century BC and likely in the 5th century and perhaps even earlier. Chinese smiths would also work wrought iron, and their access to both helped facilitate the production of higher quality steel. Steel in the Han empire would be superior to steel in the contemporary Roman Empire for example. (The Romans didn't put a lot of emphasis on metallurgy, though they did have massive mines. It would be celtic/germanic groups like the Merovingians who would advance steel making in Europe largely after Rome declined.)

In contrast to ancient China, cast iron was not common in Europe until the 13th century AD and after. So you can see there is a huge difference. While is is entirely possible to create lots of things including steel with wrought iron, having access to both allows production of steel by combing the two and allows metalworkers to make the most of the advantages of each material (mostly flexibility vs. strength). The layered steel approach Japanese swords would become famous for was practiced and possible at an earlier age in the East than in the Mediterranean/Europe.

So in the ancient world into the early medieval period European/Mediterranean metallurgy was inferior to Chinese metallurgy. I don't know how much longer that superiority lasted. As for the reasons, many have been suggested. Needham points to access to certain ores in China that reduced the melting of iron, making it easier to cast. I would also add the focus for the Roman Empire was on extraction of metals, especially precious metals, while the Han Empire seems to me to have been far more focused on metallurgy over extraction.

Chinese metallurgy formed the base of Japanese metallurgy. Since Chinese metallurgy spread to and influenced Japanese metallurgy, it seems fair to say that Japanese metallurgy would have been superior as well over the same period. Though I cannot say that with certainty as my focus was on China when I researched all this for a paper.

Sources:

Needham: The Development of Iron and Steel Technology in China (This gives a rather technical and detailed account (Needham was a scientist originally), and also places the development within a world context.)

Wilson: Machines, Power and the Ancient Economy

Finally, Encyclopedia entries I don't have on hand right now

I am by no means an expert in metallurgy so please correct me if I am mistaken!

The Knight and the Blast Furnace: A History of the Metallurgy of Armour in the Middle Ages & the Early Modern Period by Alan Williams is a remarkable work that is sadly out of print, but you may be able to obtain a copy through your library. I think it would add significantly to the background of this discussion.