As an aztec main the biggest issue i come accros mid and late game are the 2 falconet push from europeans, aztecs have very little to counter this. most arrowknight damage is blocked by the ranged resistance even with a 5x multiplier against artillery. on top of that arrowknights are expensive, cost 2 pop and you need to make a special and expensive building before you can train them. before you even have the building up theres already 2 falconets in your base.
the second issue is train time. yes aztecs have fertility dance but then you arent using your other buffs.
Coyote runners and eagle knights are super slow to train because aztecs dont get a card or church tech for cavalry training, even infantry training is slower than europeans because they dont get a church tech for them. there is the warhut training card but thats 2 cards just to get your early game units trained at the same rate as europeans. Eagleknights have no way to boost train time besides fertility dance. This is a huge issue because aztecs only have 90 militairy population to work with.
ERK are very good units, but as mentioned theyre very expensive.
another issue not very many people know about is that they take a much bigger multiplier from skirmishers than other dragoon type units take. its been this way since TAD or maybe even the warchiefs expansion.
i made a post about this issue in october: