The Aztecs are an Infantry and Monk oriented civilization.
Their free Loom frees up gold in the Dark Age, allowing them to train five militia without having to task any villagers to mine gold. This, combined with their faster military buildings, allows them to perform a Dark Age rush more effectively than other civilizations.
Their unique technology, Garland Wars, increases the attack of all infantry by four. This gives all of their infantry massive attack compared to those of other civilizations. Their unique unit, the Jaguar Warrior, benefits greatly from this. The Jaguar Warrior already has a large attack and a bonus against other infantry. When coupled with their unique technology they can defeat any other infantry unit in the game. Their Monks are also the best in the game. The Aztecs can research every single Monastery technology, and their monks receive extra hitpoints every time one is researched. In some situations, this bonus is of somewhat questionable value, but with all monk technologies resarched an Aztec monk has ninety-five HP.
Any relics captured by the Aztecs or their teammates generates gold 33% faster, which is very helpful if the player's team has a lot of relics. In the late game, they have access to Siege Rams and Siege Onagers.
The Aztecs' total lack of cavalry or gunpowder puts them at a huge disadvantage in the late game. While Eagle Warriors make decent cavalry substitutes in the Castle Age and early Imperial Age, they don't have a lot of HP so are easily outmatched by Paladins and they cost a lot of gold, unlike Hussars. While Aztec Pikemen have greater basic attack than other civilizations' Halberdiers, they are nowhere near generally as effective against cavalry. This further compounds the problem of the Aztecs' lack of cavalry.
The Aztecs have the weakest navy in the game as they are the only civilization which cannot make Galleons and cannot create Demolition Ships either which causes them to be extremely weak on water maps in the Imperial Age.