Also, the Mongolian raiders who sakced Europe beg to disagree on what is an isn't an effective sword.
The sword that did it:
An excellent weapon when you are riding horseback and striking against an enemy on foot. A curved blade utilizes the momentum of the horse to increase the depth of the cut and the strongly twisted end ensures that the sword slides out of the enemy easier than a flat blade, minimising the change of getting involuntarily disarmed by the weapon jamming within enemy armor/body from said powerful slash.
Every weapon is a compromise between cost to make, difficulty to learn and master, reach of weapon, stabbing power, cutting power and weight. In some cases, reach is a good thing (see Rapier, Zweihander), in others it is not. Two-handed swords are excellent in taking down armored opponents and far more useful against cavalry targats than a short sword. The design philosohpy behind the Japanese blades all the way from the humble Tanto to the mighty O-Dachi
is different from European counterparts. The 'mighty' katana would have been almost useless against a medieval european full-plate which was designed to protect from cutting attacks and stabs by thin swords.
Which explain why Morning Stars of various kinds were so damn effective at killing armored targets: hit somewhere near a weak point and you get a puncture. Hit in a joint and twist and the leather straps holding the armor come off. Hit the side of a shield and you gain excellent leverage to twist it out of the way or break the arm of the wielder.
Each good weapon is made for one primary purpose. The inherent effectivness of the weapon depends on the equipment it is facing as much as it depends on the skill and other equipment used by the wielder.