Why Swords of Power(TM) Don't Work
Here's a thought - what do you think of as the ultimate sword? This is another trope that shows up quite often in all kinds of media: the concept of the ultimate blade, the Sword of Power, the mystical weapon before which all others go crying to their mommies. Frequently it's got some kind of marking or decoration to distinguish it from others as well, and it's either in the hands of the bad guy, or it's stuck in a dungeon somewhere (the Legend of Zelda option), or it's being hidden or carried around by someone 'worthy'.
Usual caveats aside regarding the possibility of magic, otherworldly technology, or other Super Special Secret Sauce(TM), this is another trope that, unfortunately, doesn't work in real life. There's no such thing as one sword to rule them all. A sword is made in a particular shape because it's a compromise around what's feasible with the materials at hand, and its eventual purpose. It's all about what you give up in order to get an advantage elsewhere.
So let's start with size
Are bigger swords better? Eh... no. Not necessarily. I know this from experience. What you get from a bigger sword - more momentum in the swing, longer reach, and in theory more protection from a large crossguard - is balanced by the sheer effort involved in moving it. Bigger means heavier, and it means slower regardless of your own strength. Bigger means more inertia to overcome. Bigger means longer, and longer means you may just dig the sword tip into the ground unless you adjust your technique to handle it.
Smaller and shorter means you sacrifice reach and power for maneuverability and speed.
How about shape?
Swords can be either straight or curved to some degree. A curve makes the sword excellent for cutting, like in a horizontal slash, and you see that a lot in techniques that use duelling sabres, for example. But the curve that improves the cut also weakens the sword in the thrust, because not all of the wielder's energy can be transmitted efficiently down the blade. A straight sword designed for thrusting - the rapier, of course - excels at it, but it can't deliver a cut anything like a sabre can.
If you ever take a look at pictures of cavalry swords, for example, a lot of them tend to be curved - presumably because cutting slashes were more effective from horseback than thrusts.
The notion of the sword that can cut through anything (lightsabers aside) is a particularly prevalent one. But in reality, such a sword probably doesn't and can't exist, because all sword blades are a compromise between hardness and flexibility.
You wouldn't think that flexibility is important, but think for a moment about how swords are meant to be used. (Warning: Physics!) The blade delivers kinetic energy from the arms of the wielder to the target at the point of contact, with the intention being that the point of contact is as fine as possible in order to focus the energy and do the most damage. Ideally, as much energy as possible will go into that damage. But if the point of contact is hard, like when a sword meets another sword, or meets armour, then the energy is dissipated elsewhere - like, up through the blade and into the hands of the wielder.
Try it out with a steel pipe, or something designed to be very rigid, if you don't believe me. Tap it off something hard, like the ground, and you'll feel the shock in your hands. Now imagine that it's scaled up to the power of a sword meeting another sword at high speed, and it'll become flat out painful. It could even knock the sword right out of your hands!
This is why flexibility matters. A sword must be hard enough to do damage, but not so hard that it can't flex under an impact and dump the excess energy instead of hurting or disarming the wielder.
Hardness also matters when you're looking at the edge of a sword. The edge needs to be sharp to focus all that lovely damaging energy, but if it's too sharp and too hard, then the blade will dissipate excess energy by shattering into pieces. (Note: this is why no one makes swords out of diamond, in spite of the fact that diamonds are the hardest mineral.)
The best way to think about this is to view the sword blade as something that has to be capable of delivering and absorbing kinetic energy. Hard things deliver energy very well, because being hard means you don't yield in the impact. But flexible things absorb energy very well, because being flexible means you do yield in the impact. And a sword blade has to do both at the same time without sacrificing too much either way.
Again: Super Secret Magical Special Sauce that makes physics irrelevant negates all of this. I'm just talking about actual real world stuff. Someday, though, I'd like to read about a Sword of Power that's literally just a long, sharp, pointy thing.