1: The blade is curved. This focuses all the energy of the wielder's swing onto a single point, allowing it to more easily slice through... well, anything. The katana was designed during an era where heavy wooden armor was overwhelmingly common, so the katana is almost specifically made to get through said armor. Hence the curve. Normally curved blades are smaller, but the katana is a notable exception.
As already noted, curved swords are not for penetrating armor. Plus, Samurai armor was laquered steel. I really don't know how this wooden armor stuff started.
2. The katana is usually wielded two-handed. One hand on top of the hilt pushes forward, the other hand on the bottom of the hilt pulls back. This provides an overwhelming amount of force compared to other swords, again facilitating armor piercing.
Not unique to the katana. Any sword that can be wielded with two hands has this advantage.
3. The katana is heavier and harder to wield than a regular sword. Heavy training is required to use one, and a lifetime has to be spent to master it.
There is nothing that makes a katana harder to use than a comparable two handed sword. The weight range for both western and eastern swords is comparable: 1.5-4 pounds.
Katana are also more manoeuverable, due to the fact that the point of balance is a mere 5" from the tsuba or crossguard. (Some Western swords can be anywhere up to 8-10"!)
There were swords with a center of gravity that far forward. There were also swords with a much, much closer CoG.
This sword is an exacting reproduction of a medieval longsword. The center of balance is 2" from the guard.
Another sword, this one with the PoB at 3.5". If you'd like to see a real antique,
here is one with a PoB less than 1" from the guard. A
sword from the 13th century with a PoB at 3.7". 2.5" on
this one. The katana isn't any more maneuverable. (More swords can be seen at
http://bjorn.foxtail.nu/swords.htm, click the English button and then "Virtual Museum.")
Most swords were blunt-ish
Medieval swords were rarely razor edged, because it wasn't necessary, but they were not blunt. This is obvious if you look at the edge of a medieval sword, especially one in good condition. They are rarely razor sharp but the edge geometry is anything but blunt. Read up on this
here.