Here's my thoughts on the new battle themes:
[spoil]
Trainer Battle: Very good and catchy, loved it when I heard it in the first big Pokemon drop at the end of June. 8/10
Wild Battle: It's alright, could be better but it isn't bad. I don't really mind it. 6/10
Hau Battle: Love this one, super catchy and fitting for Hau, when I first heard it during the E3 demo I didn't necessarily like it, but that was only because we could hear so much of it, when they showcased it with the version exclusive reveal, I really liked it. 8/10
Team Skull Grunt Battle: A very good and fitting evil team theme this time around, I enjoy it more than Guzma's theme actually. 7/10
Totem Battle: Better than the wild battle theme, and works for the intensity of the Totem fights. 7/10
Kahuna Battle: Love how it feels intense then moves on to a playful and cheery tone. Works very well for the Kahuna battles. 8/10
Gladion Battle: One of my favorites. Works for Gladion and I love it when the themes have this BW soundtrack feel. 9/10
Plumeria Battle: It's enjoyable like the grunt theme, but I feel the grunt theme is still superior. 6/10
Guzma Theme: I don't like it, I don't think it fits Guzma's personality and behavior, I feel it should be a little more energetic and intimidating. 4/10
Aether Foundation Employee Theme: Enjoyable but forgettable. 5/10
Lusamine Theme: Amazing. Fitting for how eerie and evil Lusamine is and it also ties in her beauty and if you listen carefully it has a little Colosseum reference. 9/10
Mother Beast Theme: I feel it fits very well for the encounter, but I like the other version a lot more. 7/10
Solgaleo/Lunala/Necrozma Theme: I really like this theme, but I think there could've been a little more to it, love the XY legendary theme reference in there though. 8/10
Elite Four Theme: My favorite of the themes. It's absolutely phenomenal and sounds exactly like what an Elite Four theme should be. Better than the Unova E4 theme IMO. 10/10
Champion Theme: A lot of people don't seem to enjoy this one and consider it lazy, but I think it was genius to remix the main theme of Pokemon into the Champion theme. 9/10
Guardian Deity Theme: This. Is. Epic. I love how eerie and intimidating it sounds, super fitting for the Tapus with their 'all-mighty' descriptions from both in-game and dex entries. 10/10
Ultra Beast Theme: It starts out epic, then goes bizarre and strange sounding, I think it works for the beasts, but the theme to me is decent. 7/10
Red/Blue Theme: I feel this is a downgrade to the theme and I don't particularly enjoy it. 4/10
[/spoil]
Don't think I missed any, but I feel like I missed maybe one or two themes? Not including previous themes that were untouched like Anabel and Cynthia's themes.