I might be abit late to help you but for the sake of discussion here's my take on this.
A katana is a sawing weapon, Really.
No its not, its a cutting weapon.
It has microscopic serrations.
Such serrations would actually create drag which would hinder cutting power
Unlike a claymore, longsword, etc, a katana is "Drawn" over the object to be sliced, much like a good kitchen knife. (Western swords "Cleave", like a meat cleaver.)
First of all he most be speaking about curved vs. straight blades, I will discuss this more later.
Western arming and bastard swords were used to cut, not cleave. The only medieval western sword's used to cleave as opposed to cut were types like the Falchion, Dussack and Cutlass and historic reports and modern tests have shown that such weapons were in fact just as deadly as blades used to cut if not more so.
Katana are not used to strike one another in the fashion that a western fencing sword is.
I'm going to take a guess and say he is speaking about 17th - 19th century fencing blades, if which case my response would have been Rapiers were only used in combat as secondary weapons by soldiers who did not need a better blade, most Musketeers and maybe even a few Pikemen.
If he means parrying then yes they actually were.
Most Cavalry, Pikemen, Targeteers and others who were expected to fight in a melee carried better swords such as the Side-sword(also called Cut & Thrust sword) Back-sword(also called single edged sword), Broad sword(which was a shorter and stouter Back or side sword), Cutlass and Saber.
Katana have 2 distinct types of metal used in construction, and the cutting edge is VERY VERY FRAGILE. (A curse from feudal japan is "May your sword shatter and break") Katana have only 1 cutting edge. The other is blunt, and made of mild, low carbon steel. When using the katana to deflect a blow, this blunt side is offered to the incoming blade, in the attempt to shatter the enemy blade. This 2 metal composition is what causes the sword's unique bowed shape. (The two metals have different modulus of elasticity, and different rates of thermal contraction.)
Most blades are made thus regardless of where their were produced or the metal they were made from, the best swords had an iron core and steel edges.
The part of the blade used to parry a blow were the sides not the back, Single edged swords were at a disadvantage to double edged swords in that if your blade were to become dull you would be forced to fight with a dull blade as opposed to a double edged you simply switched edges.
Due to the fragility of high carbon steels, a katana needs to be "Folded" and "Laminated". Basically, this means that part of the structural integrity of the blade is maintaned by the softer, mild steel in the back part of the blade, because it is folded in with the high carbon, fragile steel in layers. The mild steel bulks up the blade, but makes it so that it wont shatter if it strikes poorly, and gives it a little flexibility it otherwise wouldn't have.
The Celts were folding their blades before Christ.
Katana's historically were actually very fragile when compared to blades used in Europe or the middle east, it was always used as a secondary weapon to the Polearm and Bow(actually quite like the European Rapier)
And high carbon steel is not fragile, Japanese high carbon steel was because their iron ore was fragile due to its poor quality, modern steel making techniques are used to correct this flaw in Modern Japanese steel.
Imaginary Adamantine does not suffer a high fragility, like high carbon steel. As such, it wouldnt need lamination, could be made absurdly thin, and could be used absurdly fast. It would be like giving "Super paper cuts" rather than "Chopping".
This is mostly just for the nerd in me, but the harder a metal is the more fragile it is.
This is why we see blades made from high carbon steel as opposed to tungsten.
Basically, a super paper-thin nano-serrated razorblade that never goes dull, and is 5ft long. Due to not needing to be laminated, and not needing a deflecting edge because the cutting edge cant shatter, it would\could be a 2-edged straight sword. (Though curved would permit easier use.)
Curved blades are not easier to use than straight, they are about the same.
The idea that Curved blades are better for cutting and straight is better for thrusting is not entirely true.
The reason why people think that curved blades are better cutters? because the bottom part of the blade makes contact before the top focusing all the power of the cut onto that one area, if the entire area made contact at the same time this would create "Drag"
The science behind this theory is correct, but what this theory does not take into consideration is that a straight blade is not actually straight as an arrow, "Straight blades" were usually A: Tapered, which means that the blade will slightly narrow from hilt to tip and B: had conclave edges which means circular as opposed to "Razor straight", which means that the bottom part of the blade makes contact before the top...
It is also interesting to note, that blades that were not tapered and did not have conclave edges made to be used entirely for thrusting such as the Roman Gladius, are still capable of cutting a person's head or arm off.
Curved blades can also be used to thrust to great effect, especially if it has a "Hatchet Tip" type blade.
The Advantage that the Curved blade had over the straight was it was easier to pull out of its sheath, the advantage that the straight had was that it was aligned with your arm and therefore had a better center of balance, but these differences are actually quite slim.
Both types could be single or double edged.
It is interesting to note that it is commonly thought that in the 18th century curved blades replaced straight blades in European armies, this is actually not true, as a matter of fact only light cavalry such as Dragoons or Hussar's used curved blades, Heavy Cavalry who were expected to charge home fought with straight bladed Broad swords.
Infantry fought with both.
Another really interesting fact, After the wars of the "Japanese invasions of Korea" the Chinese copied the Japanese ōdach, one of the first things they did was straighten out(but not totally eliminate) the curve, http://en.wikipedia.org/wiki/Changdao