Not to hijack the thread but the above is not entirely correct. It's true that the fighting style in Europe was somewhat different. There were many different styles of swords used in Europe, some highly specialized and some "all-purpose". Up until about the mid-13th c. most European swords were relatively thin, excellent cutters. Later on as armor improves, swords become longer and stiffer and there is more emphasis on thrusting.

Contrary to the popular belief, medieval European swords were for the most part quite light, no heavier than a katana per comparable blade length. Also, they were not meant to actually cut through armor. If you had to fight an armored opponent you'd ideally only use the point and target the weak spots in armor. But the sword was not in fact the primary weapon against armor, there were better, specialized tools for the job (mace, war hammer, pollaxe etc.).

The trick is, most European swords were either slack quenched or quenched and tempered to a relatively low hardness. In effect, the edge wouldn't last that long but the blade was very springy and tough.

The Japanese on the other hand never really figured out the tempering process. Hence they used clay and used a complex method of patternwelding, taking soft iron for the back of the blade and steel for the edge. A very similar process was known in Europe but was no longer used after the early middle ages because it wasn't cost-effective and you could get better results with more homogenous steel.

As a result, the edge on Japanese swords was fully quenched and very brittle while the back was very soft and tough - but not actually flexible because in effect it wasn't heat treated at all. It would bend under heavy stress rather than spring back. So metallurgically speaking, it was far from an ideal solution. The only reason why it worked is that the Japanese used lighter armor, largely lamellar made of hardened rawhide. A 15th or 16th c. Japanese sword would've been fairly useless against a European plate harness. Of course, it could still be used with great effect against an unarmored opponent. But so could a European sword from the same period.

Metallurgically, the very best medieval swords may have come from Iran and India. In those parts of the world relatively homogenous steel was already known in the antiquity, hence the famous Damascus blades. Billets of crucible steel were also exported to Europe. They were very expensive because of high production cost but could be forged into excellent blades.