Besides, a decent European sword would cut any katana in half then carry on through the armour behind it like it wasn't there.
Had to look it up, because it seems unlikely.
For one thing to cut through another thing, it has to be harder than the thing it's cutting. So we can go look at which is harder, a European blade or a Japanese one.
Bunch of hardnessess of European Middle Ages to Renaissance Era swords
1850's Katana (you said any Katana)
Hardness on both are about the same on both (Mid-high 40's HRC), therefore you couldn't easily cut through a Katana with a European sword.
The problem isn't really one sword cutting through another, since as you can see in the chart, even modern steels can't really cut through the hardest old steels very easily. It's more-so the impurities in the steel which will cause weak points in the sword where it will shatter or break when stressed. Also, as you increase hardness, you increase the carbon content in the steel, which decreases the flexibility of the sword, which will also lend it to shatter or break when stressed.
Katana's and European swords were both designed to have different hardnesses along different parts of the blade so that they were both flexible in the places they needed to be and hard in the places they needed to be.
Their main differences seem to be the effort put into purifying the steel. Japanese iron was lower quality so their forging process took forever, European iron was plentiful and they mass produced swords. That's basically it.