Comparing a longsword and a katana is like arguing between strength and speed. The longsword is heavier, but doesn't hold its edge as well. The katana is quicker, but doesn't have the same kinetic energy of a heavier weapon, meaning it doesn't have the same brute force as, say, a claymore. In Europe, where battles were fought upon horseback or using a sword and shield and plate armor, a heavier blade had the best chance of doing damage, unless you were nimble enough to pierce the gaps in the joints. However, that extra weight of sword, shield, and armor made one slower. The European style would be to focus on defense through heavier armor, then.
In contrast, the Japanese style focuses on speed and mobility. Even their heavy armor was quite light compared to plate armor. Because of this, they focused on a style that involved quick strikes, and an instant turn from parry to attack. A lighter blade, with an edge that was very sharp, is able to do more in such situations than a heavier blade.