When it comes to weapons, everything is a trade-off: if you add more weight, the impact force will be higher, but you lose on nimbleness and control. A mace can be really effective against a heavily armoured opponent but it is very forward heavy, so you cannot control it as well as you would control a sword. In this regard, extremely sharp weapons will lose on the durability side.

One of the main weapons of Aztec troops was the macuahuitl, which is, broadly speaking, a wooden plank lined with obsidian chunks attached to it with resin. Obsidian knives or blades are scarily sharp, and can be sharper than steel blades, but here we come to the trade-offs. Obsidian is basically glass, and broken or chipped pieces of glass are mighty sharp, everyone knows that. However, glass is very brittle. Hit a plate armour, and the obsidian will shatter to pieces. Hit some unprotected area, and it will cut phenomenally well (some Spanish sources like Bernal Díaz or López de Gómara claim these obsidian "swords" could decapitate a horse in one strike).

Plate armour, made of good tempered steel will resist the impacts of obsidian blades without any problems. However, in the rigours of the tropical climate in Mexico it can be a liabilty due to the heat, causing its wearer to tire and sweat. This is one of the reasons why conquistadors would resort to using just gambeson, a type of armour made of several layers of linen or cotton that would normally be worn under the armour for padding and extra protection. Gambeson is not much different in its nature to the cotton cuirasses the Aztecs used. Just by the sheer number of layers (around 10), it gives some good protection against swords or arrows.

Claiming that steel plate, gambeson, swords, lances, and crossbows are inferior to obsidian weapons, cotton armour, and obsidian pointed arrows is rather preposterous.