As someone who owns a celtic broad sword and a skramasax (a type of single-eged Germanic short sword, also known as a
seax[/URL], scramaseax, or scramasax), I've gotta disagree. The only real "advantage" I see a double-edged sword having is cutting on the back swing. Other than that, Katana all the way. Aside from the metallurgical construction of the weapon, The fact that it is a single edge
with a nice, thick spine means you can parry with the back of the blade and not risk damaging the edge. That is beauty of single edged swords. And the fact that the blade is curved means that the force of the cut is delivered with a much smaller surface area, which equates to a deeper cut with less effort.
As far as I know you have never really heard of warriors who hold their Katana on the blade and then smash the opponent with the crossguard/hilt/pummel... where as that is known to happen with straight double edged weapons here in Europe. You basicly have a club doing that... was quite effective against other people with plate armour on. I mean if you compare the hilt of many swords, with a warhammer... it's not all that different. Half swording is a thing, and it makes the use of the weapon very versatile, not only as a kind of club, but also for precision stabbing with the blade, AND as a cutting weapon against people with soft armor, or no armor.
With the Katana you don't really have that. I mean it is possible to do it... but the "club" type of strike I mentioned above would probably be nowhere near as effective with a Katana, since I do not think that they have the same kind of weight in their hilt as most european swords had.
As for parrying... it is not to uncommon to parry with the flat of a sword either, and most european swords are more flexible in the lateral direction, more so then what most Katanas are... which makes a difference, since a Katana would be more likally to break due to that. Also, due to Katanas much harder edge, they where more prone to cracking and pieces of the edge compleatly breaking of, much more so then most edges used in europe. And it did not matter to much if the european swords edge lost it's sharpness a bit, or gashes and such... they can still cut pretty well. I have seen blunted european swords (where you could drag your hand along the edge without cutting your self) cut through those rolled mats that they often use to show how sharp the Katana is. Yes, they had to use a bit more force, and the cuts where definatly not as clean... but cut the mats they did anyway.
And yes... the Katana is very good at cutting... but that only really applies to "soft targets"... so either no armor, cloth/fabric armor, and soft leather and such. I don't know how well it would do against properly hardened leather (I have read that it can be harder then wood apperantly)... but against anything metal, be it chainmail or plate armor... it is going to struggle. Stabbing works against chainmail of course... but the same can be said for regular european swords vs chainmail. The Katana is going to struggle against plate armor no matter what (as much as they try to show a katana cut/stab through plate online, I highly doubt it would really do much against properly made plate armor).
So really... the Katana has basicly the same kind of problem that for examle a longsword would have against armor. Yes a longsword is not as good at cutting cloth and leather and such, as the katana is, but at the same time that longsword is going to give a concusive strike instead. Since all of the power in the swing will go straight into the target, rather then most of it disapearing. In either cases the fight might be over with one good strike... be it by a cutting katana, or a concusive strike from a longsword.
I am not saying that one is better then the other. What I am saying is that the Katana is not superior to other swords. I am also saying that in general there has always been a huge amount of exaggerations been thrown around when it comes to the Katana, and at the same time a huge amount of underating and general claiming of being inferior when it comes to what the european swords are capable of.
And when it comes right down to it... if a sword can make nice clean perfect cuts, or not, matters little on the battlefield. It matters little if the opponent died from a perfect cut, or a bonecrunching strike that more ripped apart the flesh then cut it apart. Dead is dead no matter how it happend. I doubt anyone goes around after a fight and says "oh, look at that strike, look at how clean that cut is... amazing!".