First of all, curved is much better for cutting. You have a larger surface area for the edge of the blade. There's a reason why cavalry swords were always curved. They didn't have to swing so much as simply hold their sword out as the curved edges would draw across flesh and slice through, whereas a long sword would simply get stuck into whatever it hit. So that bullshit about technique or whatever is just that. Curved swords effectively cut better than straight edges.
Now, I'm not a big fan of the Japanese, but military historians widely regard both the gladius and the katana as the two best developed swords in the world. They each excelled in their respective roles: the gladius as a short, thrusting weapon used in close combat in conjunction with the scutum (the roman shields that basically covered the entire left side of the soldier); and the katana as a two-handed weapon cutting weapon (but yes, it can also thrust, and I did practice Shinkendo for around 2 1/2 years -- I even got to spar with Toshishiro Obata for a couple minutes when he visited our dojo). The longsword is a long, straight, double-edged blade. It didn't cut as well as the katana, and as far as thrusting, yes it was long, but that's what made it unwieldy. For thrusting, you only needed to penetrate three inches into your opponent's midsection or torso. The gladius did that very well while allowing you to fully control your shield (which was the real workhorse). Also, because it's short, it's very easy to retract the blade after you hit your opponent for another thrust (likely at another opponent). In a crowded melee, you'll probably have to drop your longsword and draw your short sword or dagger after you pierce your opponent. As for the katana, you just cut through your opponent and your blade was free to strike at another. Of course, the katana wasn't designed to cut through opponents wearing full plate, so I couldn't really argue about it's effectiveness against a knight, but it definitely cut through conscripted soldiers with ease.
As for knight versus samurai, I don't care as it's just Deadliest Warrior crap. You can pretend to think you know who will win, but you really don't. Yeah, shields and shield walls were a huge part of western warfare, and in the east, samurai believed that only cowards hid behind shields and were ready to die for their lords in combat. Now, maybe the samurai were a bit naive about the effectiveness of hoplite shields or scutums, but their fanaticism in combat isn't some easily measured attribute. And anyway, samurai were trained in the use of many weapons (spears, bow, short swords, and hand-to-hand combat). Restricting a samurai to a katana, or even a knight with just a sword and shield for that matter, is like restricting LeBron to lay ups and Curry to dunks. Both fighters were highly trained in many different weapons and could use them effectively in the appropriate situations.
Anyway, I'm sorry but longswords versus katana doesn't seem like even a fair comparison. Because both weapons are wielded with two hands? A katana wielder could easily close in on a longsword and disarm the wielder due to the comparatively unwieldy nature of the weapon (when compared to the katana). The stance of the wielder, and the curved blade, which allows you to deflect more easily would make quick work of a longsword. Now if you want to throw a shield into the mix, you might as well ditch the sword altogether and grip the shield with two hands. A scutum versus a katana, now that'd be really interesting.
I never got where this unweildly crap comes from. Long swords are not cumbersome, they are agile and half swording was a very effective thing in closer range. Closing in and disarming a skilled sword fighter is not gonna happen easily.... ---