Maya is the most consistent, as you will ALWAYS research Theology, and you will ALWAYS be able to build pyramids. The other three count on their terrain to be effective, but for the most part, you'll always be placed in a good spot to take advantage of it.
I voted Iroquois for the potential. I have played games where I completely dominate because of their production. It basically goes like this: Goddess of The Hunt pantheon because of the amount of Deer and Fur found in forest, and go tradition. This means you can grow from camps, have a high population for your 4 or 5 cities, and this means you can use the longhouse to work as many forest tiles as you can. Each forest will have three hammers, and four once scientific theory is researched. Going on quick speed, say hello to building wonders in 5 turns during a Golden Age. Coupled with the fact that your land will be forest heavy, if someone tries to get smart and attack you, your cities will be a lot easier to defend, and you can move through to the edge of the forest before they even step foot in your lands. Building 2 solid units every 3 turns, and you'll have a large army in no time.