And remember the Native americans and Aztecs? The Spanish and English had guns. The Aztecs and Native Americans didn't. Guess who won in the end?
The South American indigenous civilisations frequently butchered the hell out of the Spanish conquistadors in fights on their home territory. Guns at that stage, impressive as they were, were less effective than atlatls and macahuitls in dense jungle (as was their cavalry). What killed the Aztecs was the fact that they were an Empire based on fear and intimidation (which worked pretty damned well) and Cortez was very good at stirring up their subject city-states into rebellion. Ultimately, this was not a winning strategy.
Another difference was the mentality of the soldiers on both sides. Aztec warfare had, for the last 200 years, been all about slave-taking and intimidation. The macahuitl's design was not to kill but to maim so that subjects could be brought back as slaves to fuel the economy and religion of the Empire and keep everyone playing good little vassals. It was a very effective system for a very long time. European warfare was mostly about killing the other person as quickly as possible, leading to the development of weaponry and tactics aimed at killing over maiming.
Were guns important? Yes. Were they more important than the internal stresses and politics of the Aztec Empire, the major differences in tactics and outlook and the diplomatic cunning and greed of Cortez? No, not by a long shot.
And with that, take it to Fluff. Don't make me compile a full essay with references, because I can.