Civ Ability:
Dynastic Cycles (China): This ability is an effective 20% discount for any tech or civic whose Eureka you complete. That’s absolutely insane.
Free Imperial Cities (Germany): Districts are essential to everything cities do besides growing themselves and building units, and Germany will be able to have more of them than anyone else (dramatically so in the case of small cities).
Amazon (Brazil): Assuming jungle start-bias does what it needs to, this will dramatically increase the availability of adjacency bonuses, making Brazil the most effective civ when it comes to early game science, culture and faith.
Leader Ability:
People of the Steppes (Tomyris): If an important game mechanic (building units, for instance) is balanced at its default level, it’s very difficult for it to not be overpowered at double that level.
Religious Convert (Mvemba a Nzinga): Being able to ignore an entire game mechanic and still reap most of its benefits, provides a great deal of flexibility, especially when each city is limited in the number of things it can focus on
Trajan’s Column (Trajan): Early bonuses are disproportionately powerful in a game like civilization, and it’s hard to get earlier than this. Trajan will unlock early civics earlier than any other leader, and every one of his cities will get its early infrastructure completed faster.
Unique Infrastructure:
[I found this the hardest category to evaluate, as it features a lot of numerical bonuses that are difficult to put in context at this point. I ended up choosing exclusively unique districts, on the grounds that they allow each city a mostly free extra district in addition to their explicit effects, but depending on how easy it is to work lots of non-farm/non-resource tiles, some repeatable tile improvements (the Kurgan, Mission and Ziggurat come to mind) could also be competitive.]
Royal Navy Dockyard (England): This district seems to be doing most of the work for the English civ (thematically as well as power-wise), providing economic bonuses to colonies, as well as naval power.
Hansa (Germany): The default industrial district allows you to make mining-focused cities that already have good production better at it. The Hansa allows you to add production to cities that otherwise lack it, a much larger comparative advantage.
Acropolis (Greece): Most civs will need wonders to gain powerful culture adjacency bonuses, but Greece can do so without any such investment. Such an ability would be immediately decried as overpowered if it applied to science, and culture in Civ VI will do much of what science has done in past editions.
Unique Unit:
Eagle Warrior (Aztec): This unit looks like a UU and UA rolled into one. Early game economic/development advantages are more important than any but the absolute best combat bonuses, and free builders are about as significant a development bonus as you can get (This assumes builder stealing will be harder than worker stealing in Civ V. If it isn’t the Eagle Warrior’s competitive advantage will fall off dramatically.
Legion (Rome): Forts were relatively weak in Civ V, but then again they also took time to build. Legions have the ability to dramatically reshape the battlefield mid-combat and do so while also being stronger than any contemporary unit in a straight up fight.
Saka Horse Archer (Scythia): The developers seem to be intentionally avoiding any units comparable to Civ V’s Keshik, Camel Archer or even Horse Archer. The Saka Horse Archer is the closest we’ve seen, and while it lacks range and hit and run ability, its potential for first strike focus fire, with no retaliation from the target, is quite significant.