Dont know if you'd ever need this, but here's a breakdown why if you want supernatural cutting power, the Japanese way is actually better for it than european swords.
You have probably heard of Japan's shitty native iron, forcing them to adapt to their limited supply by becoming really, really good at using that steel for blades... But it actually goes deeper than that because the way these blades were forged as a result means that they were made with way stronger backsides(the non sharp parts), ehich means that you can out a lot more force behind the actual cut.
Meaning yes, it's sharper than european swords, but it's also capable of harnessing more force into the cuts.
On the flipsides, this also means that even if the sword was made from superior European or indian steel, the sword STILL would also be way more likely to break, because the same factors that allows for more force applied, also makes the blade way more riggid in its construction, meaning that one bad move will snap it in half.
Bad yes, but not so bad if you fight in a place where shields arent a thing.
By contrast, the European swords like the norse longswords that became the base for... Every sword ever made in the west, is made in such a way that it's base is way more springy and flexible, because in a culture where shieldwalls were the dominant way of fighting, you simply cannot afford a weapon that will lodge itself in the enemy shield.
This was such a common thing that what little we know about direct norse martial arts is in large part about taking advantage of people doing exactly that, which is one of the reasons the relatively soft norse shields had that metal part in the middle to protect the hand istelf from both arrows and melee strikes.
But what this also meant is that the Norse and other europeans never really went all in for a stronger, single edged blade with more cutting power, because it would be useless in shield based warfare.
Completely opposite of japan.
Only once guns became a thing, and shields became obsolete as a weapon of war, did the single edge with a stronger back become part of European mainstay swords.
Early european sabers weren't quite there, but you can easily spot where they began adopting more eastern designs for weapons to be used at horseback as shieldwalls became a thing of the past.
Incidentally, you might have heard that sabers and curved swords are better to be used on horseback because the momentum reduces the chances of it being caught and snagged in the human body.
This is true, but as you might have figured out from all of this, ALL the same reasons that genuinely made the katana just flat out better at cutting things than a longsword applies same to a saber.
The lack of that age old springy back in fabor of a more rigid, harded spine means you can channel more force into the cut, which are also now from horseback, and often delivered while the swinger is in a charge with all the momentum behind him.
Best of both worlds really. The superior Shot and pike cavalry of europe(which reached its peak in Poland-lithuania in the form of the winged hussars), and the genuinely sharper blades of the east.
That said, the same cons still remained, with the saber being way less durable and easy to destroy than a longsword... while the actual European succesors instead shifted to specialize into newer forms of killing.
The more advanced metalurgy that forged cannons also allowed for way bigger swords, so professional soldiers adapted the double sided blade to just be bigger, creating the claymore and zweihander massive longswords so big they could be used both as blades and makeshift short pikes if need be.
And for the one handed option, they invented the rapier, pound for pound the deadliest blade ever made.
No joke, if you want the deadliest weapon ive mentioned so far, the rapier is it. Once big shields were gone, the europeans could go all in on stabby stabby, no matter how thing the blade was... which incidentally made a sword it was ridiculously easy to kill someone with, because as the romans proved with their stabby stabby gladius, being stabbed is way more instantly lethal or decapacitating than being cut.
Hence it became to go to for both soliders of the non zweihander variety and duelists.
In fact, the one time where there was serious conflict between Eurpean and japanese melee fighters, when some spanish marines fought on a ship boarding against japanese pirates, the rapiers made short work of their Japanese counterparts.
And for added bonus, it was immensely adaptable in mixing with pikes and guns, making it, again, the inarguably most successfull battlefield weapon on this list.
Katanas, longswords, zweihanders, and sabers were weapons used by specialized units, not the main weapon of the day, which was generally guns or spears.
The rapier, not so much, because at the height of the swedish empire, the swedish Caroleans, the strongest army in the world pound for pound, ALL had one at hand in every battle, be their other weapons pike or gun.
They were used in every battle, and to be accepted into the army had to be sharp enough to cut a feather mid flight, and strong enough(Springy steel to the rescue) to not break or be permanently damaged by the weight of a grown man stepping on in and trying to break it with weight and applied force(Something no katana or saber could have replicated).
Mayhaps not as sharp, but you dont need to be sharp enough to cut steel to kill a man.
And this, is a short overview of the difference between eastern and western blades.
Hope you someday might find it usefull for your writing. If not, i still hope you found it fun to learn.
I always love hearing about physics and tactics in action, and this definitely applies!
Both actually fuel a lot of my own action writing, as I find the tactical back-and-forth of anything from a single brawl to an entire war to the most interesting aspect of the conflict. It's the "problem/solution set" (as I like to call it) that makes such a thing feel more like storytelling than sportcasting. And finding ways to incorporate physics is always fun, as it helps increase the plausibility and can even make for some cool surprises.
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