The only real downside of a rapier that I can see here is that it's not heavy enough to punch through armor. That's why the rapier was generally a civilian weapon, not a weapon of war.
That said, a rapier is just faster and more agile. With combatants of equal skill, the rapier wins out.
The thing is, I've never thought of katanas as particularly excellent swords. It was sharp, sure, but only really good as a slicing sword and not against armor. The steel quality wasn't that great, the blade was too thick for effective use against armor, it was generally shorter than a European longsword (even for the same weight), could stab but lacked reach, had hardly a crossguard or pommel and just the single edge.
Katanas weren't bad, otherwise the Japanese might have used something else during the, what, 900 years the katana was in use? They were versatile weapons, sure. But they weren't the ultimate sword they were often portrayed to be, nor were samurai the ultimate warriors.
That said, a rapier is just faster and more agile. With combatants of equal skill, the rapier wins out.
The thing is, I've never thought of katanas as particularly excellent swords. It was sharp, sure, but only really good as a slicing sword and not against armor. The steel quality wasn't that great, the blade was too thick for effective use against armor, it was generally shorter than a European longsword (even for the same weight), could stab but lacked reach, had hardly a crossguard or pommel and just the single edge.
Katanas weren't bad, otherwise the Japanese might have used something else during the, what, 900 years the katana was in use? They were versatile weapons, sure. But they weren't the ultimate sword they were often portrayed to be, nor were samurai the ultimate warriors.