This is gonna go stupidly in-depth, so prepare for a Wall of Text which discusses the meta of the meta before actually getting on my tier list.
Generally speaking, the best Civs in Civ have either been the ones that had the best, most flexible bonuses or fit the game's most optimized meta better. To analyze in Civ V, the top tiers were Poland, the Maya, Babylon and Korea. Poland was stupidly versatile, and quite literally got free stuff. However, all the other three were Science civs, be it seizing a massive advantage in the early game in the case of Babylon, or just outsciencing everyone as Korea. While the Maya did not reach the same "level" of Science as early as Babylon or as powerfully as Korea, it still was a Science powerhouse punching a ton above its weight, and for the science Civs, it was easily the most versatile of them. Drop a few levels below, however, and England, China, the Huns and the Zulu, pure war civs based around overwhelming your opponents with massive strength, showed up in the radar. Meanwhile, the more versatile civs were also featured here, such as the Inca, Ethiopia, the Shoshone and Russia; in addition, the Civs whose entire point was to be good at one victory type and that did so masterfully, such as Brazil or Greece, also appeared fairly high. On the other hand, while there were other, more versatile Civs down the list, they didn't perform so well due to not being as powerful as they need to be.
In short, the key in Civ has always been having three good scores: versatility (how many options are open to you on a particular game), power (how powerful your options are), ease of usage (how easily can you get those bonuses) - all of that being analyzed to the meta of the game.
Based on that, I'll rank the Civs we've so far, the 20 of them, on a scale of 1 to 10 on each ranking.
By the way, sometimes the lack of ease of usage, especially if compensated in the other areas, can make a Civ much more engaging. It was very common for modders in the Civ V community, which though about the design of Civs a lot more than other modders, to consider how you can make something engaging - by having a very strong focus in one area, with a certain direction of things you have to do, Civs became much more interactive as you had to push for specific things, do certain specific goals rather than just follow the same old paths as it's always been.
S Tier:
Germany (Versatility 9, Power 10, Ease of Usage 10) - Frederick's bonuses are extremely powerful and easy to use, although there is very much a warlike style to them. While warring can be the most powerful style (and it generally is), there should be considerations that it isn't always the path followed for whatever reason. Besides, any beginner can pick him up and play him decently well - his bonuses always apply.
Pericles!Greece (Versatility 10, Power 8, Ease of Usage 9) - What is one of the best begginer Civs in the game, Pericles shows up early on as a good, more passive, Diplomancing Civ that tears through the research tree. Their power isn't spetacular in all areas (save for Plato's Republic), but the great majority does its job extremely well, and it's very well balanced around a plethora of paths possible, save for a slight focus towards Culture - but it's like a Science bonus in Civ 5, you're basically getting more progress faster.
Gorgo!Greece (Versatility 9, Power 9, Ease of Usage 9) - Pericles' more agressive version. The fact that she has a more warlike bent does detract a bit from the possibiltiies available, but she's still very versatile and her LUA is very useful during the early game. Her bonuses, however, are far more powerful that Pericles' are - they come in earlier, they have more effect, and they're very useful throughout the entire game still. Again, very versatile, very useful, very cultural in a way, but due to its bonuses require action it's not as versatile as Pericles.
Brazil (Versatility 8, Power 10, Ease of Usage 7) - Pedro II does well in literally every area, although he prefers to be a bit more Science-like (with a bit of luck, he's also very Religious). With arguably the highest yields in the game, only rivaled by Tojo, Pedro's can be amongst the best. On a not-so-bright side, however, Pedro has a small issue of being almost restricted by where he settles. Since he's so limited in that way, he loses a lot of his Ease of Usage and Versatility.
Japan (Versatility 7, Power 10, Ease of Usage 8) - Hojo's in a bit of a weird spot. He's very much a versatile guy, don't get me wrong - but he's even more shoehorned into being this Military-Culture hybrid than Gorgo or Frederick are. He can have the best yields in the game if he plays his cards right, and building things for half cost is very powerful, even if they're not the main things that people follow. Basically, Hojo can can be stronger than anyone, but you need to follow a very specific path with him to squeeze every drop of power you can from him.
A Tier:
Rome (Versatility 9, Power 8, Ease of Usage 7) - Trajan's strength comes in free Production, free Roads, free Gold, nearly free everything. He can go very settling-wide, defend or attack whoever's at his borders, while also growing his cities. He does a bit of everything, really. Why isn't he higher? He has to go wide. Say you're in an awful situation where going wide is not possible. Is Trajan still decent? Very much so. But if he doesn't get a strong start rolling, he can't reach maximum potential. His power is hampered by the fact that if he doesn't get a strong start, he drops in the rankings a fair amount.
Scythia (Versatility 5, Power 10, Ease of Usage 9) - Tomyris is an example of a Civ which does something really freaking well, but it only does that something really well. Her Faith game, while above average, is meh. But dear Lord can this woman ever wreck stuff. Some of the largest armies in the game allow her to overwhelm cities with sheer numbers - and let's face it, she's not really gonna stop for anything in her path. I'd compare her to the Huns in Civ 5. Very powerful, obsecenely so in the early game, but due to a few bonuses that carried on they could capitalize on early conquests better than anyone. Past a certain point, however, not really.
China (Versatility 8, Power 7, Ease of Usage 8) - Qin would be a great Civ - the +1 free Builder charge is one of the strongest bonuses in the game, much like increase in Eurekas and Inspiration effectiveness. They're also very very versatile because of that. Afterwards, however, while a good, defensive turtle Civ, Qin lacks enough power to truly punch into the S tier.
Russia (Versatility 10, Power 6, Ease of Usage 7) - Peter's main issue is that he has no focus. Allow me to clarify. Peter's powers in every area allow him to gobble up territory, generate tons of Great Works, never really fall back behind anyone and even defend decently well. However, were one of his focus actually in the same direction in a way that would make you actually win, he'd lose some of his Versatility for a massive power trade off. In any case, Lavras are massively strong. Peter is, IMO, one of the best Civs in the A tier for Deity, becoming S tier as it can maximize its LUA bonus, making it actually be worth something.
Arabia (Versatility 8, Power 8, Ease of Usage 6) - Saladin does decently in every area. He can always guarantee a Religion, he can make use of the Faith he produces, he can generate plenty of Science and a good amount of Culture, he can fight decently well. But his Ease of Usagew drops him from being an S tier contender - you actively need to pursuit things with him to make him work properly, especially in a way that's engaging. It's not so much as that he needs X to truly work, but if you want to do anything with him, you'll have some focuses and goals you don't really have in other games. That makes it a bit harder to use him in a game.
B Tier:
Aztecs (Versatility 6, Power 7, Ease of Usage 7) - Montezuma's not really all over the place, but he's got goals and directions that very much limit him. He's warlike, he loves his district and builders, he does decently with faith, he wants to have as many amenities as one can. It's all very interesting and engaging, but compare him to other Civs, and he pales a bit. However, notice that he's labeled as "B tier" - all Civs in here are very much usable and can dominate entire games, they're just more bound to one single goal, one single idea in general, although not always.
Kongo (Versatility 4, Power 9, Ease of Usage 5) - Mvemba's issues stem from his path being very weird. He's definitely a Tall Civ that's also very Cultural-focused and will likely win through Tourism, granting a fair amount of power. But being gimped completely in the Religious Victory department, with a Cultural runaway, Mvemba can be absolutely shutdown, requiring him to follow other, less effective paths for his more peaceful, culturally-focused style of gameplay.
Egypt (Versatility 8, Power 5, Ease of Usage 5) - Cleopatra does a bunch of stuff decently well... and nothing particularly great. She's very good at conquering and can get tons of incoming trade routes, she can do very well culturally and she can grow a ton too. Her only real issue is that none of this versatility is enough to carry her own weight across the finish line to win the whole thing purely on its inherent abilities.
Sumeria (Versatility 5, Power 8, Ease of Usage 5) - Gilgamesh likes to go in and go agressively. The Ziggurat's nothing to write home about, but it does its job decently well. Gilgamesh can also help his friends with conquest, which means you'll want to join someone who's as agressive as you are, but then again, it's nothing to write home about. The War Cart and the UA really carry Gilgamesh with their overwhelming power early on. He's got an issue of being very good at the early game and needing to ride that wave, because otherwise he kind of falls off compared to other Civs.
India (Versatility 7, Power 4, Ease of Usage 6) - Gandhi's... weird when it comes to analyzing. He's so variable that it's hard to pinpoint what's his goal. Honestly, the main thing you'll want to do is grow tall and gain tons of Faith, which grants him some useful versatility. But seeing as his abilities are too dependent on others, Gandhi's power isn't really obvious.
C Tier:
England (Versatility 3, Power 7, Ease of Usage 5)
France (Versatility 6, Power 6, Ease of Usage 3)
America (Versatility 4, Power 6, Ease of Usage 4)
Spain (Versatility 4, Power 6, Ease of Usage 3)
Norway (Versatility 4, Power 4, Ease of Usage 4)
[WARNING: Unfinished, will finish tomorrow when it's not 1:30 in the morning]