I disagree. Aside from supermedics, they are excellent at early rushing. refer to my RPC: MONTY game.
Read the fine print

(I mentioned that)
Non-medic uses of Jags.
1) They can man forrests and jungles which are abundent enough early on. Cut an enemy road between cities or resources and man a Jag or 2, very tough to reconnect.
Usually I find it more useful to use the fast movement of any group of units to get to the city faster and attack sooner in order to face fewer defenders and defense bonuses.
2) They need no iron, just the tech. This means you can jump on an AI very fast, often before they get axes up.
Usually by the time you finish researching bronze working, you wouldn't be too far away from hooking up a source of copper. I guess you have a point if you end up without copper anywhere nearby and you're prioritizing speed above all.
As do axemen. (and we'll assume that you carry at least one spearman in your stack for protection, especially once you've noticed horses in the hands of the enemy)
4) MONTY is agressive so they start with 2 free promotions, combat I and Woodsman I allowing the most versatility of any UU except perhaps Churchhills redcoats. Both of those free promotions stick with the unit throughout the game if it's promoted.
Monty's axeman would also start with Combat I (which also lasts throughout the game), so that's a moot point. Woodsman I free promotion allows the Jaguar to unleash its two potentials:
- Supermedic (Woodsman III, Medic III combo)
- Superrush (as opposed to a regular rush with units* that will continue to benefit you in the long run)
* - Axemen
5) Woodsman II Jags move twice as fast in enemy forrests making them great at hitting behind the lines (second only to Keshiks IMHO).
Hitting behind the lines is not that useful, IMO, especially if you're using them for rushing (which you should be if you're using them at all). Usually it's more useful to just march right onto the cities and take them. Of course, it's very useful to flank the city to make sure it doesn't get additional defenders, but there's no time to wait when you're rushing (especially as there's no waiting to be done without siege weapons). By the time you reach the point in the game where it's useful to wait when you've arrived at the gates of the enemy city (such as you now have catapults), the enemy has likely nicely countered the Jaguars with some Axemen, or more ironically, Swordsmen, and you can likely build some horse archers (which have strength 6).
6) They are more efficient at attacking cities than axes because of the +10% city attack.
I noted that. I say that this small bonus is far outweighed by the complete versatility of the axeman.
Enough of bashing a very good (not the greatest I agree) UU just because it is 5 instead of 6 combat units.
Unfortunately, combat odds are very shifty. A slight increase in ratio can yield a comparatively much higher change in odds. So yes, 1 strength out of 6 is big. At least swordsman can put up a fight against axeman by using city raider. Jaguars have no hope.
Like I said, superrush (which I don't feel is a good idea in most cases) or supermedic. And let me tell you, I love playing Aztecs for the supermedics! It makes a huge difference to have your units heal (almost completely) in two turns in enemy lands!!