Huayna Capac, Pacal, and Sitting Bull are indisputably the best choices to win the game? I can understand you liking these guys, but... That's a pretty easy claim to dispute. If you aren't playing on small cramped maps, their super-early hitting power oftentimes don't do much for you at all... I know playing on huge maps all the time, a Quecha (spelling?) rush often isn't feasible due to raw distance early on, and the opponents likely having Axemen by the time you're even close to done with one Civ. A protective Civ is still a very tough nut to crack too, and there are plenty of those kicking around.
Chariot rushes from the Egyptians/Persians are every bit as effective for early game dominance - I often bump off two to three civs with Ramses easy, seeing as the CPU doesn't build many spearmen.
I like Pacal a lot, and recognize that Huayna is a good guy as well... Sitting Bull is not my cup of tea. Any which way, there is plenty of grounds to dispute the dominance you claim they have.
The fact is Aftershafter I play exclusively marathon games were each epoch truly counts and you can make a diference, as an empire, in just one period of the game (tech tree). This is a limitation to my so called claim.
Of course Egypt ,specially Hatshepshut for her culture expansion grabing resources advantage, and Cyrus are excelent for early rushes as well, but they are still horse dependant for this matter ;you can get it much later than you wish or not at all.
With Huayna, Pacal II or Sitting Bull their advantage is guaranteed, for the latters you may even get BW in a tribal village (worth 40-50 turns of early research in marathon) without the dangerous need to have copper nearby nor a worker to conect the metal. I once got bw with Pacal while researching hunting. By the year 2000 BC I had already subdued 4 civilizations, including the obliteration of Summer (protective) and Persia (who never got to grab those horses within a second city spot.. as if). This was a huge continent with around ten civs which I ultimately dominated by the middle ages. Emperor level, no bragging intended, seriously.
Moreover, with Pacal your Mayan empire becomes almost immune to chariot, imm, war-chariot rushes. And well, you can already imagine what is it that Sitting Bull doesn't need to fear from.
Needless to mention, I'm leaving out of the topic their traits and UBs here, perhaps you care to discuss After..
If I had to choose I'll keep the good and old Pacal II anytime, but the other two are close enough.