The Aztecs actually improve on marathon for the following reasons:
1) Thier growth advantage relative to other civs improves due to thier UB. And this improves thier production ability. And science. So thier relative production is better on Marathon than on standard just because of thier UB. And the longer the game goes, the more advantageous it becomes. And lord help anyone if thier capital starts with a lake within one or two hexes.
2) While thier pts per kill doesn't improve, they have a longer time to kill units, and given that SP cost more in Marathon, this gives them an advantage (as it does France). As the number of Aztec barb hunters increase, thier ability to get though the SP increases. And, they tend to get through the honor tree faster if they aggressively barb hunt, adding more culture from garrison units.
3) Once Monty gets about 4 jags/archers hunting, his ability to advance SP is simply amazing. And between building jags, usually converting a scout to an archer from a goody hut, and buying a jag with gold, it just doesn't take that long to four hunters. And this just keeps snowballing. Once he's through the honor tree, hunting barbs or war then generate money as well as culture.
4) Last, but not least, if you generate about a dozen jag earlier and upgrade them all the way to mech infantry, you usually have a very deadly force of mech infantry and can inflitrate through woods/jungle better than anyone else - and recover some damage after an attack. So thier special ability comes into play through the entire game - not just at the start. Making them superior Swds/LS/Rifle/Mech Infantry.
Regarding the others mention, my experience has been:
Rome. Situational. No iron or limited iron and you have a big problem. While I like Rome (I'm a builder), the iron issues a gamble.
Germany. You get a lot of benefit from your unique ability BUT you run into supply problems early and often (the only civ I know that does). This limits you ability to generate money and expand & upgrade your army. If you can get pass this, you can dominate from the middle age forward. And spearman upgrade to the lansnkenight is soooo cheap....But it really hard not to cripple your production early due to supply limitations. And you have to hunt to generate funds, but if your already at the supply limit, you may just go over if hit that barb camp AND generate less gold, which hurts your ability to generate gold and production........
Greece. For whatever reason, I usually end up with a poor starting location and no easy expansion route. So I have problems with this civ.
Persia. One of my favorites, just not what I would consider the best on Marathon.