That is probably the worst video of its kind. Swords are swords, and all cut and/or thrust to varying degrees depending on intended usage. No sword can cut plate armour, period. Where the longsword shines is versatility. It cuts well, it thrusts well and can deal with a wide variety of situations. You can carry it on your hip (though often they were carried in their scabbard like a walking stick). A specialist weapon might be better in a narrowly defined context: for example, a rapier thrusts better, but is useless against armour. A katana may cut slightly better, but suffers in reach, and cannot be used reversed like a warhammer the way a longsword can. A pollaxe is better against armour, but you can't carry one around while strolling around a medieval town. Having two edges is very handy if one is heavily damaged too. Those are things the tests (as flawed and deliberately biased as they were) didn't even consider.
-Mark