Ink, I know you're an okay guy, but it is you and Anodizer who are arguing from a position of *profound* ignorance regarding this particular subject matter. It is not really you guys' fault, since between pop culture, the Renn Faire/SCA scene, and poor historians, there is a lot of BS floating around on this rather obscure subject.
Suffice to say, when I compared preserved/quality replica European cutting swords against their Japanese counterparts, the weights were similar, with the European swords actually being somewhat lighter in relation to their length. It is not surprising that swords designed for powerful cuts will have a similar mass, a cutting sword must have just enough blade to support cutting geometry, without adding undue mass. If you think about it, you will realize the idea that any culture was stupid enough to make inordinately heavy swords is absurd. Not only would excess weight decrease the sword's maneuverability, but velocity is a component in the force of your attacks. Too much weight would prevent the warrior from accelerating his sword effectively under realistic condition, actually reducing striking force.
Metallurgically speaking, European swords have a resilliency that most traditional Nihonto lack. If you have poor edge alignment while practicing tamashigiri, you can easily end with a bent sword. Some very old school dojos keep a device known as a "sword" straightener on the wall.... By comparison, from at least the Viking period onward, European swords can typically be flexed at least 30 degrees or so out of line and return to true. This allows these swords to be thinner in cross-section than is typical for a traditional Japanese sword.
How sharp were European swords? From studying the techniques of the European teachers of fence from the 14th-16th centuries, it is apparent that many of the techniques they taught for use against unarmored opposition were relatively quick, light strikes and slices that would require a decent edge. The idea that Europeans used a "blunt" sword because of armor is wrong. Sword-edge sharpness is irrelevant when attacking iron and steel armor, you are not going to cut it to any effective extent. (Full plate armor is such effective protection against sword strikes that re-enactors today engage in essentially full-contact sword fights wearing the stuff.) However not every opponent on the battlefield was armored head-to-toe, and against leather, cloth, flesh, and bone, edge sharpness is *not* irrelevant. The only sort of "edgeless" type of European sword I know of is a rare, specialized type called an estoc that was forced with a narrow, diamond cross-section and specifically used as a sort of short spear/leverage tool against fully armored opposition. But as I say, this type is rare, understandable considering you can execute the same types of techniques with a more standard longsword.
What is their cutting potential? The ARMA used to have a video of a member removing the head of a freshly-killed deer with a single, one-handed strike from an Oakeshott type XIV, a typical blade-form from around 1300, pictured below.
The part that stuck in my mind was that it was actually a less than full force, "pulled" blow because the tester was being careful not to strike the floor! Preserved examples of this type of sword are typically around 28'' in the blade and weigh in between 2-2.5 lbs. It is something of a "compromise" design between cutting and thrusting, and the taper gives it a very pleasant balance.
