It's a little bit of both.

Iirc, Japanese iron was usually in sand form, gathered, rather than mined. So the raw material was smaller and contained less natural carbon than mined ore.

(Though nobody had near the advantage of Indian steel from the Damasc region - Damascus steel naturally had more carbon in their iron and it made for very high quality steel at the time.)

Anyway, at that time Europe had similar techniques for making iron into steel and normalizing the carbon. They would use more resource-intensive techniques, like stacking rods of wrought iron in a furnace with charcoal, then working the carbon-infused rods to distribute the carbon evenly.

That works great when you have access to millions of square miles of forest (for charcoal) and loads of iron ore.

But it's not really about whose steel was "the best", it's just that the "folding" technique was a metallurgical process and had no impact on the quality of the sword (except insofar as it was turning iron into steel).