Incas and Aztecs are both pretty powerful, in my experience. They are both growth-oriented, but the Incas are more expansionist (yet defensive), while the Aztecs are more war-friendly.
The Incas should stick to mountain-y spots. Terrace Farms brings you insane food, and their UA guarantees that your expansion isn't slow (in fact, the Incas are good for following either Liberty or Tradition). Furthermore, their roads are free if you stick them on hills. Their UU, as cool as it looks, isn't useful. Finally, the UA is actually better than it sounds, providing better gold, better mobility all around, and some good defensive strategies in combat.
The Aztecs are amazing near lakes, but the Floating Gardens are also good if rivers are all you have. Jungle start is a tad rough, but Aztecs have a surprisingly slow start, anyway (you'll want to build at least 5 Jaguars before Metal Casting). The population growth kicks in once you have Floating Gardens up and running, at mid-game (I once founded a city near a lake, on a desert, insta-built Petra and paid 400 Gold for instant Gardens. "Insane" barely describes how fast that city grew). Furthermore, you can actually profit from every war, while the Inca don't.
One weird thing they both have in common: both Jaguars and Inca Warriors can freely move in forested hills.