It (a katana) is sharper (than a longsword), the steel is tempered so the edge of the blade is harder, and harder steel is the sharper an edge it can keep. It's the same concept as a titanium knife can be sharper than one made of bronze. I have put a good amount of time studying Katanas, as they are my favorite of weapons.
Katanas were not tempered. They were differentially quenched to harden them. This is not the same thing. And no, hardness does not equate to sharpness, or even "potential" sharpness, in any way, shape, or form. Sharpness will be largely relative to the edge geometry of the weapon, and, well, how well it was sharpened. A bronze sword can be as sharp as a steel sword, or could be as sharp as a titanium sword for that matter. Ie if they all have the same edge geometry, they can all have an edge that is one molecule wide (ie, same sharpness). Hardness relates to how well they keep their edges under use (within reason, brittleness comes into play).
So yes, katanas do indeed have a harder edge. measuring typically about 60'ish rockwell (lower for the rest of the blade. Their cores are rather pearlite in structure, making them quite soft- vs the harder martensite layout of the edges). For comparison, european longswords typically have about 50'ish rockwell. In all honesty though, its really not much of an advantage. Yes a katana can keep its edge longer, but a longsword is going to keep its edge "long enough" to be more than useful for an entire battle (or multiple battles). Its important to remember that swords were sidearms, and not primary battle weapons- Their use was limited, they were back up weapons. Not main melee weapons.
And on the topic of quality. Yes, the metal in a katana was grossly inferior to that of a common european blade. This is of NO fault of the japanese, at all. The iron they used to construct their swords largely came from iron sand. It was very impure, and contained a *lot* of impurities, and the temps at which they were capable of getting their tatara furnaces to was limited to about 1500 degrees, meaning they could no remove all the impurities. Europe by comparison had much better ore to work with at the same time period, allowing them to create higher quality swords in general. Its also worth noting that europe readily imported some of the best steel in production at the time from the east. Something japan was relatively unable to do due to their geographical isolation. "Good" quality steel was a very limited and expensive commodity to use, especially for swords. The majority of the metal that came out of their tataras was low carbon steel (almost iron) known as hocho tetsu. The better quality/higher carbon stuff (Tamahagane being the more famous of the metals, but nabe gane, which has even higher carbon content, is worth mentioning as well) was produced in small amounts per yield, and as such its use was primarily limited to the construction of the edges, or laminating skins of the sword. The majority of the sword was constructed from the hocho tetsu metal. Or frequently, entirely (Despite the popularity of the whole mixing of metals thing, many swords were cranked out using just generic iron/low carbon steel. These non-laminated blades were largely known as maru blades).
The sad truth is, historically, katanas were actually relatively
inferior swords, compared to a lot of the swords in use around the world (NOT in all regards of course mind you, theyre not completely without their merits and do some things quite well. As with most things, its all down to the context). Compared to longswords (which seems to be the common comparison), they were notably shorter in length, giving you less reach. Due to the metal used, and how they were simply quenched/hardened and not tempered, their spines were relatively soft, meaning that when they bent, they stayed bent, versus a common european blade which would simply spring back into shape. The hard edges, because they were harder/more brittle than the rest of the blade, flexed at a different rate than the rest of the sword, and where prone to cracking when the sword did flex. If they flexed much further the edges were prone to separation from the rest of the blade along the hardening line. Tips in particular were very prone to breaking off (Weather or not a katana has its original tip, a replacement, or was reground is a huge consideration when appraising historical swords) because of this. To combat this they made their swords quite thick to reduce the chances of flexing. This made them quite good at stabbing flesh, but it also made the swords heavy for their size. Your average katana was only mid 20'ish inches long in the blade. A typical longsword was closer to 40. Despite this, both swords weighed about the same, averaging about 2'ish to 3'ish pounds. They had poor hand protection in comparison, using what is essentially a small disc compared to a longsword, which has iron bars protruding out a few inches in either direction (Quillons). Longswords were counter weighed with a pommel (Which made an excellent weapon, either in follow up strikes, or sometimes as the main focus itself. Wielders would flips their swords around, holding them by the blade, using the pommel/quillons as a surprisingly effective bludgeoning tool), and had a point of balance typically a few inches away from the crossguard. Katanas had their point of balance a few inches further than this typically- Making them a bit less nimble in the hand (Please note not completely a bad thing. This was a trade off, as it gave them more impact on hit).
The assertion that they were sharper is VERY arguable. A lot of people like to cite their curvature as being an advantage, but under scrutiny thats complete bs. Katanas, despite being curved, areant really all THAT curved. Most european "straight" swords, due to their shape, geometry, and taper, have curved/angled edges, despite having a tip in line with the handle. When you measure this a typical european "straight" sword has an edge angle of about 8'ish degrees (a measurement quite common with all cultures who made "straight" swords, amusingly enough). Typical katanas literally only measure a few degrees more, in the very low teens. Some actually have even straighter angles than common european swords. Compared to more notoriously curved swords, like tulwars and shamshirs, which can measure up to 40-50 degrees of curvature, and we really put things into perspective (And the idea that curved cuts better than straight in its own right is rather dubious. Im glad to cite references upon request to support this, and if youd like to claim contrary, please do the same. Id actually LOVE to find proper evidence that supported this notion). The thing is we know longswords were sharp, AMAZINGLY sharp, we only need to look at the historical treatises that were used to train techniques with these weapons to see what they were expected to be capable of doing (
http://historical-academy.co.uk/blog/wp-content/uploads/2013/04/Ms.Thott_.290.2º_079v.jpg http://historical-academy.co.uk/blog/wp-content/uploads/2013/04/Ms.Thott_.290.2º_123r.jpg) Like these techniques demonstrating how to remove someones hand (It is
no easy feat to remove someones out stretched hand that is moving about in the air capable of moving as you put force against it). And this isnt to say katanas werent amazingly sharp. They were, and they ARE great cutters, but longswords are as well.
I can go on, but you get the point. If you (or ANYONE) would like sources to *any* of my claims, please ask- I am more than glad to provide. Books (Most of which can be read on google, the ones that can not be i will provide links to acquire them via amazon), shorter/easier to read journals, or if youre more interested in fast-food sized nuggets of information documentaries, to some interesting youtube channels- With specific videos/people, ranging from a historian, to hema (hema is type of sport where the goal is to recreate historical uses/competitions for swords. They focus on how the weapons were REALLY used historically, studying various sources such as training teatises to comprehend how they were really used practitioners, hema instructors (one in particular has been instructing since the early 2000s, and not only does he have his own club where he regularly teaches, he annually hosts the *largest* hema/hema like event every year in the uk), to people who make a living out of dealing with weapons. Etc and etc.
Fwiw, im a *huge* katana fan, it was my passion for them that drove me to learn about them as much as I could. How they were made, why there were made in the fashion they were, how they were used, etc. It was an eye opener once the mysticism/"magic" was peeled away, but I still admire them greatly. Cheers and give yourself a cookie if you read all of this
As far as D20 topic goes, either make them martial and copy the stats of the longsword, or make them exotic and copy the stats of a bastard sword (Which historically, were the same thing). I wouldnt want to be hit by either of these weapons- The damage they do is going to basically be on par with these. even if one DID have a drawback compared to the other, from a "meta-gaming" perspective, making one statistically better than the other, and having the same character cost all said and done, diminishes the desirability of the other for no real reason. This is how I typically run them in my games anyways.