Guys in the blades episode they made numerous mistakes.
For the Longsword it was a 18th century sword used for duels and was thus way to light use in actual combat.
The armour they used the swords on had the strenght of a piece of paper.
And for the ice a Katana's blade is thicker than a longsword and that is why it can cut through the ice so easily.
But this doesn't make it more lethal than the longsword. A longsword was designed to cut through bones and in the proces shattering them leaving a nasty wound.