Oh no, a soundtrack discussion. Welp, time for a longer post!
Rather than forming tiers, I might just list my favourites from each larger pack.
Starting with vanilla, I like Scythian theme the most. Duduk is simply an amazing instrument, and I prefer my darker and mysterious, yet powerful themes to themes of overhelming energy (looking at you, Brazil). Scythia also has one of the few good atomics (mind you, while they are adored by most of people, I am not fan of atomics. It's very easy to make them sound bad, and industrials mostly do the best job at showing grandeur of the Civs at their peak

). Other vanilla civs that I like very much include Japan, the US, Russia, Egypt and Rome.
The DLCs have given us several interesting themes, but Persia stands out. Santur is such a delightful instrument, and Persia has one of the few good atomics in the game. I also enjoy the Polish and the Indonesian theme.
Rise & Fall brought us some good and some less good Civs soundtrack-wise. Mongolia stands on their top. Mind you, Civ V Mongolian themes are probably my favourites from the game, and hearing Urtin Duu again in the First look made me unbelievably happy. And even though I prefer the Civ V version of the Mongolian theme, I have to admit that the fact that we got morin khuur and throat singing is very nice. It has the darker, yet powerful feel I enjoy so much by the Scythian themes from vanilla. And the fact that the music sounds like horse galloping makes it even better. I also have to praise the Zulu and Georgian themes, the Zulu for having the cheerful feel of a certain track from the Kongolese soundtrack I adore (
late version of Mama Munu Dile). Which is kinda ironic, since they're one of the most militaristic Civs in game

. The Georgian soundtrack feels spiritual and powerful. Their industrial theme makes me proud that reddit and this community memed Tamar of Georgia into the game. Their only lacking thing are their atomic themes. While Mongolia managed to get a rather good one, the Zulu one, while not necessarily bad, is not remarkable in any way. And Georgia has probably the worst atomic in the game.
Gathering Storm brought us a fantastic soundtrack. Maybe save for Phoenicia, which I find somewhat unremarkable. Hungary (one of my favourite medievals in the game, and a very great industrial), Maori (I enjoy every single version, and I'm fan of both Pokarekare Ana and the haka), Sweden (their lovely industrial managed not to make me disappointed after the sweet theme Sweden received in Civ V), Canada (I do not really mind any theme, I'm not really bothered by their anthem, and I say that they have one of the best ancients and medievals in the game), Ottoman Empire (a nice set of instruments, also, it has powerful singing in it), Inca (one of the themes, if not the one theme where I'll say that ancient is the best) and Mali (their industrial/atomic has probably my favourite opening of all themes in game. Oh, and kora is one of the sweetest instruments Civ VI has introduced to my ears) all stand out in some way to me. If I were to choose my favourites out of those though, I'd have to go with the Ottomans. While their atomic theme is not really remarkable, their ancient is great, their medieval isn't bad either, and I have to say, their industrial is my single favourite track in this game. It feels so powerful, and so immersive. As if I suddenly appeared in the lively grand bazaar, surrounded by people, spices, persian carpets and other colourful goods in the city of Constantinople during the times of peak Ottoman power, and the power is eventually demonstrated by their great janissary armies, marching through the city, singing the powerful song one can hear in the track. Plus, I have a thing for oriental things, music included.
New Frontier Pass brought us two themes so far - Mayan and Gran Colombian. I would like both Simón Bolívar and Lady Six Sky to appear in my games as often as possible, because I like both of their themes a lot. Especially Bolívar. I fell in love with the Gran Colombian industrial theme as soon as I heard it in the NFP anouncement video. Actually, it might as well share the place of my most favourite single track in the game with the Ottoman industrial theme. Their flute/guitar ancient is enjoyable and the Pajarillo part of the medieval theme is delightful. The only thing the Mayans do better is their atomic. Too much bombastic percussion in the Gran Colombian one

.
I keep saying that the themes keep getting better and better with each pack. I wonder if Mr. Knorr and Mr. Rizzo will manage to bring something that would topple the position of Gran Colombia as my favourite of this pack. If there is a civ I'd bet could have the potential of doing this, I'd say Byzantium would be the one if it gets its magnificent chants like the ones in Civ V. Provided that they are included in the pass. Right now, I'll be somewhat impatiently waiting for what Ethiopia can bring.
I can't say I'd hate any theme, especially so much that it would make me ragequit. I wouldn't even say I'd dislike any, even though some have versions that can go one one's nerves (like what the Georgian atomic one does for me). I listen to civ music quite a lot. And, well, I simply have to say I managed to find something I like by every theme. Not necessarily every version, but there's little something in at least some variation that I like. For example, I've mentioned that the Brazilian themes are overfilled with energy, but
the ancient theme that plays by Pedro II's diplo screen is very charming to me. If I'd have to name one theme as my least favourite though, it'd probably be Germany.