To what extent were the Europeans more technologically advanced than the indigenous people of the Caribbean and Mexico?

The Spanish conquerors had steel swords, lances, daggers, helmets, and armor as well as horses, guns, and canons. While guns and cannons were slow and rather primitive, gunpowder explosions created a great psychological effect. The Spaniards had ships, maps, and compasses, while the Native Americans had much smaller boats and relied on human memory for their navigation.
The Spanish were also able to exchange information by means of writing; they could request and receive more soldiers and supplies from the Spanish colonial administrators. Printed reports about the conquests and the acquisition of new riches in Mexico and Peru attracted a stream of European colonial settlers. The reports also facilitated new investments in colonial enterprises from European bankers, such as the Fugger family.
Soon the gold and silver mines that settlers created in Mexico and Peru provided rich rewards and enabled Spain to finance its colonial administration and engage in global trade across the oceans as Spanish coins minted in America became a world currency.