The Aztecs lacked horses and attack dogs. The Spanish by contrast had perfected combat with both. Both proved decisive over and over again. You're correct in asserting that guns weren't decisive - although initially he noise and visual display of firearms were a significant factor in confusing and frightening the Aztecs (especially the common people and subjugated indigenous groups).
I think the horses proved useful in some situations (at least to scare the people who had never seen riders), but then the number of horses was somewhere between a dozen at the start and never more than a hundred. And from what I've been reading their use in battle was often hit and miss because the cavalery often didn't have enough room to be effective.