The tradeoff is they don't require iron!!!
That's the main deal!!
Imagine this:
2 Civs at war, Aztecs & Romans.
1 Roman Preatorian pillages the ONLY Iron mine of Aztec.
Montezuma: Let them pillage! We have mighty Jaguar Warriors!! Unleashed them!!
1 Jaguar Warrior strolls over to the ONLY Iron mine of Rome & pillages it.
*Screams are heard*
Messanger to Caesar: Rome is doomed, Caesar!!! We can no longer produce Preatorians!!
Caesar: My, my... Not expecting this from Montezuma... Interesting...
But I digress
Without Iron forget about Swordmen. This case, Rome will need to fall back on producing Archers or Spearmen and is on the defensive. If the Aztecs can hold out the Iron source and mob them with enough Jaguar Warriors, the result is predictable.
My 2 cents