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Although I consider that their skills could not be compared since they hardly faced each other in battle due to the geographic distance. Besides their weapons/technology, geography, leadership, training and other factors contribute to winning a battle. This makes it difficult to determine which was better, but at least we know that each have its own merits and they were great fighters in their own time and place.

Anyway, I find it interesting that someone try to analyze this carefully although I believe there is an inevitable bias (Well, I think every writer has its own bias in a way):
The European Medieval Knight vs Japanese Feudal Samurai
Katana vs Rapier

Personally I'd say the knight, as their swords were actually meant to break weaker weapons (paper-thin katanas, anyone?), and they had superior armor, plus a feature that the East just couldn't seem to grasp: shields. But for the sake of argument, I'll just say it's impossible to know for sure because neither renaissance knights nor feudal era samurai (as far as I know) exist anymore.

And those who are biased to say samurai because of watching anime shows such as Samurai Champloo and Rurouni Kenshin... quit being biased. That kind of speed is highly exaggerated and physically impossible for any human being to achieve, no matter what race.

The katanas are not that thin, but katanas could break. In fact, there's a certain kizu (sword damage) name for a dangerous katana damage which cannot be repaired and at the brink of breakage. However, I must also note that the katana would not easily break off in a single battle. Its folded technique (in forging it) supposedly make it more tough (but the Eurpeans also have discovered a similar technique although I cannot say that it was prevalent). It depends on how much and how hard it has been used. There was also a certain technique in using the katana to avoid damage. In the practice of slashing a rolled tatami, it seems to have a slightly slanted movement.
But if we compare katanas with medieval European swords, the European swords seem to have more durability.

Contrary to popular belief, samurais were not merely sword-yielding warriors because they were originally mounted archers.
Sidenote: There was a known battle in between the Mongolians (who had mounted archers) vs knights (I forgot which king it was under, but I think they were English since they used English longbows). In that battle, the Mongolian won. It is important to note that not all knights were able to afford the expenisve full-plated armor as many of them used chain mails. The Mongolians used the strong Mongolian bow which penetrated through the chainmails and the Mongolian armor was brigandiene type that composed of layers of silk, which was a good protection to the English arrow. (Note: Silk is also used in Kevlar armor used by policemen). The mobility and efficiency of the mounted archers gave them a huge advantage over the knights.
Note: Silk is also used in the samurai armor, and not all samurai armor were wooden. They also developed a metal armor but I think it is near the time when firearms are being introduced in Japan.

Besides these facts, the battlefield is often the most disregarded factor, which could actually dictate the outcome of a battle. Some Roman soldiers drowned while crossing a river because of their heavy armor. A better example of how the battlefield affects the outcome is Napoleon's battle at Waterloo. It was raining so their superior artillery became inefficient. Moreover, they were on the lower portion of a sloped mound. When they charged towards their enemy on the higher grounds, they were not aware that there was a larger enemy army behind the peak of the field. They had to retreat upon realizing that they lost the battle.

To put it simply, before we could ever decide on the victor, it is important to take note of the factors- type of armor, weapons used (besides sword there are bows&arrows, naginata/polearms, etc.), battlefield location and circumstances of the setting, whether the fight is one-on-one or army vs army, mounted or unmounted and so on. I guess, I would rather study battles in history than try to guess what may have happpened since historical records can show various aspects of the battle and how they won.

I am just curious to know what is the criteria for considering something as a superior material. Technically speaking, both sowrds are made of steel, but these have differences in the percentages of elements such as iron and carbon. For me it is not just the material, but how the material is used in order to maximize its potential.

Katanas have a higher carbon content than the European counterpart and the Japanese have discovered the different levels of steel as seen in their kitae techniques in which they differentiate hard and soft steel (soft steel have less iron than the hard steel). The use of these two kinds of steel are actually beneficial to preserving the katana since it helps the it endure hard blows- the harder the steel is, the more brittle it is (similar to glass/ceramics which are hard, but brittle).

An important thing to note is that katanas and European swords were used in different ways. The European sword may be left dull because its weight helps in giving more force to the strike. The knights were fighting with armored knights so cutting with sword is not an issue since they have the mace to do the job of crushing the enemy armor. At least, the blunt force of the sword to the helmet can knock out the enemy. Since the longsword is double edged, the knights can swing it back and forth without worrying where the edge is. They technically don't worry about sword sharpness. The one weapon they keep sharp is the dagger because it is used to pierce some enemy flesh uncovered by the armor- usually in between the joints.
On the other hand, the katana is designed to be sharp. Compared to the double-edged (European) longsword, the katana is single-edged and has a good backbone (mune)- this may primarily be because it was designed to cut. One edge is to be kept sharp while the backbone acts a support. (I have also seen a video in which the katana damaged a kabuto- samurai helmet. I suppose its focus on sharpness can also be the reason to the damages on the sword.) Another interesting thing about the katana is the way it is curved compared to the European longswords. Many theories were said about it, but my hunch is the fact that samurais were cavalrymen so it just seems fit. (Notice how cavalry swords are often curved). The katanas do not need to be as bulky as the Eurponean swords (which is mostly one-and-a-half or double handed) because it can rely on its own sharpness and the momentum of the samurai (especially for the cavalry).

Since there is a different usage, there is also different techniques to it that each mastered. There are certain stances and moves depending on the sword used so I presume, both the samurai and the knight would be surprised at the technique of the other.

Ah- pity; this would have been amazingly helpful when I almost did this for my first semester research project. blaugh

Thank you for the information- I find this a fascinating topic!

Good News! I am actually going to a swordfight today that will pit western steel against japanese weaponry! I will post later on the fight!

I'm a bit curious about the details. I think the broadsword beating the katana can be expected. But headbutt is not something I'd expect rofl - I guess that's what happens in real fights because there may always be something unexpected happening.

Katanas are good when used for cutting cheese broadswords will just mash it. cheese_whine