It was made of better elements, but the quality by my understanding was dodgy. There were many, many more practitioners of the art. I recall reading about how some of these emerging smiths put whole batches of blades out with impurities that made the blades prone to fracture. In Persia and Japan, only a select few masters and apprentices were responsible for the entire production. Consistent product, even if it was higher in, say, tin could be argued as a better product even if many more physical units roled out of Europe. The absolute top tier blades came out of Northern Europe and around the Mediterranean. They pioneered and perfected the process even before the Japanese started in the art.

Absolutely. Finely processed and smithed metals can be made pretty well anywhere. The Europeans of old had a few tricks up there sleeve as well. The Nords, for instance, made blades of world class quality. Your typical broadsword however wasn't hammered out for refinement and quality, it was produced quickly with intention of replacement/repair after a respectable service life. In Asia, metal armour wasn't a concern, they needed something sharp enough to cut leather, but forgiving enough to take the abuse of contact with Mongol battle gear. Blades were handed down over generations without much maintenance aside from oiling. A similar situation led to the processes further west.