I have a book on the subject, and the advantage in the folding process is combining two features. Western swords tend to be made out of either hard or soft steel. Hard holds a real good edge but is more brittle, better for something like a rapier. Soft is durable but doesn't hold its edge very well, but you need the durability for a big smashing claymore. A katana's folded steel allows for the benefits of both with a hard edge and soft core. (Relatively speaking metal is still metal)
That and the katana's shape allows for better slicing, but still is decent for thrusting.