Come on, did anyone think I'd write reviews for Bandori but not review ARGONAVIS? Didn't think so.
And yes, it is my second favourite series. I just have a much stronger emotional connection with Bandori.

Any major plot points past ep3 (the full formation of the band) are under spoiler tags.

A quick note and helpful reminder: While the series and the main band technically share the same name, the band's name is in title case, while the series name is in full uppercase. Hence, for any times I talk about either, the band is "Argonavis" (or, for short, "Argo," as I use in this review) and the series as a whole is "ARGONAVIS."

Music:

Freakin' awesome. Only one insert and ed1 are meh, but the rest are all good to amazing.

When it comes to the bands' music overall, I find Argo's are hit-and-miss, but the anime really just has their hits~ And the aforementioned meh songs.
A couple of their songs – particularly the ones in episode 9 and 10 – just have so much meaning to them, too, which is just–

And the other band that shows up? They have very few inserts but they are some of their best songs overall~ And the opening and ending they do too are just–

The performance in episode 8 is, visually and musically, my favourite in the show~ That song was literally my favourite from the series for a while and even now is... probably my third or fourth favourite~ Maybe fifth, since the true climax insert in ep13 has just been creeping up on the spot of best in the anime, though visually it's not as stunning...~

Yeah, they use one of the less-awesome songs, Goal Line, a lot to the point that, more than the opening, it could be considered the theme song of this part of the series. But it's still a pretty good song, though not amazing...~ Also it just means a lot to me...~

And, the "meh" insert I mentioned earlier is... a pretty relevant one, with some strong emotions, despite its mediocrity.

Story:
Honestly it's kinda rushed at the start, but it slows down later to give the main drama time to work well, unlike the "drama" of the first couple episodes.
Arguably the main band quickly finding the members could be a plus, to mostly avoid the opening/ending animation(s) spoiling anything, say, halfway in to the season...
But when in episodes 2 and 3 the existing members were reluctant to let the other characters in the opening animation join, that argument loses its value.
I mentioned this issue in my review on Bandori s1. Though at least here they rush through that and get some actually good parts a bit quicker~

The actual drama starts around episode 6 and it's mostly character-focused, so I'll go into it later. Episode 10 brings in some less-character focused drama...

Spoiler, click to view

The members of Argo relied on luck for a while by getting some very good opportunities. But when the band's luck runs out in said episode, they end up writing a song with the line "Something like luck can't be called good or bad." And yeah, it makes sense. After all, how can it be "bad" when it simply strengthens a groups' friendship and resolve? For a while I thought that line mostly applies to how they missed out on DesFes... but it could also very well apply to Banri's condition and, quite possibly, the offer Ren received. The former was a stroke of bad luck and the latter was one which most would consider incredibly fortunate. However both could easily break down the friendship built up between everyone or help strengthen it.

Now, some of you may notice, in my note, I say it has six out of nine common music anime cliches/tropes I've noticed. But do remember this – *cliches and tropes are never inherently bad.*
Besides... literally only one of them is actually a seriously plot relevant one. And, the key part, the way they handled that plot point was vastly different to the other instances I've seen. In the way it was brought in, in the way everyone handled it... I felt it when seeing a different instance of it play out. How different the drama was even though the source was literally the same, because of the different characters and different circumstances and stuff...

Now... the biggest flaws in the story. One, is just how much they try to do in such little time. Some plot points don't have as much focus as they might have needed, ideally, and a couple characters, too. As for the second big flaw... which I'd say is probably the bigger one – the ending.

So this tag's going to be going in-depth about the finale:

Spoiler, click to view

So, a big part of the drama in the second half was Banri's condition after an accident. In ep13, the lingering effects rear their head and he ends up in a brief coma. The rest of Argo make a new song and stream it to him, *pray*ing for him to wake up. And he does. Roll credits.
This also comes right off the back of the climax performance, which makes it feel a bit clunky anyway... but that's not the biggest issue.
That, is how literally the moment after Banri wakes up, the insert ends and it goes to credits. That just makes it feel so awkward and weird... all they really needed was maybe an extra scene or two, totalling to at most a minute, probably, where Kenta calls Wataru going "It worked" followed by a mini celebration from the rest of Argo's members and/or one showing Banri up and about, maybe walking into Submariner, and then suddenly caught up in a group hug where everyone goes "I was worried!" and such. That would've made it feel a lot more complete.
And even if the scenes needed turned out to be longer, they could've cut the ending song, too...

It is still fairly emotional, despite its flaws, though.

Characters:
First off, this show doesn't have a generic cheery, always bubbly, super-extroverted main character!

But rather, that personality type goes to the guitarist and leader of the main band, Yuuto.

#####I forgot why I took such a relatively late gif of him and nothing else... He's kinda annoying at first, at a glance being that stupid archetype, so I don't care for him much. But, as with any character in this series, there's more to him than just that. The drama I mentioned in episode 6 shows that.

Spoiler, click to view

He actually has very little confidence in his skills, to the point he says he's quitting the very band he started. While, like I said, I don't care for him much, the scene where every tries to convince him not to quit is kinda emotional~ Not quite enough to make me tear up, but still.

How about the main character, Ren?

He's a shy but passionate and cute guy whose problems... appear to end merely at "Last time I sung with anyone no one else was serious." I wanna say he's got at least a fair bit of charisma – he got the two members that joined after him to open up about their problems and helped them find their places in the band, after all – though I may be saying that slightly out of "he so cute third best boy"...~ Wataru, the bassist and lyricist... gotta say he's not very interesting. He's just kinda fun and provides a good balance with Yuuto being more realistic than the overly-optimistic leader. In episode 7,

Spoiler, click to view

it's stated he has an inferiority complex towards his older brother. Honestly, if he were in any other series, he'd probably be one of my favourites 'cause I seem to like that type of character a lot. But in this series, where almost everyone has more complex and unique problems... he just feels kinda boring.

In short, he plays a necessary role, but isn't too memorable outside of that. Rio, the keyboardist and composer, is a genius who can do anything really well and he has pride in that... but he also seems to hate his talent for not being able to find anything to get passionate about since he's equally good at everything...? I'm not actually certain on that but in both his likes and dislikes there's "himself" so... He's... there I guess. Banri, too, doesn't have much presence, for the first half at least. While his wish for money is at the core of his character, said point doesn't get brought up much later. It takes a while, but there are some emotional moments with him at the centre~ The events from ep8-10, in particular.

Spoiler, click to view

In the post-credits scene of ep7, he got caught up in an accident. The following episode he assured he was fine and that the doctors already said he could leave before his bandmates even showed up. But later that episode something seemed odd about his hand during the show... which was foreshadowing for literally the very next episode, where Yuuto finds out there may be some lasting effects from the accident which could be serious... and he pretty much says it's okay to kick him out if it does turn out that way. Both that scene and the scene in ep10 where he's like "I don't want that to happen" are pretty emotional~

As for the other band? Only really one or two of them have any plot relevance, so I'll just go over them briefly. There's a pretty guy who constantly gets annoyed at his bandmates and is kinda fun, a Chuunibyou ~~(who needs more focus)~~ and... sigh a flirt whose lines are pretty much all about women. Oh how I hate him. There's also the serious, calm, glasses-wearing guitarist and leader whose plot relevance is doubtable.

Then the one who certainly has relevance. The vocalist, Nayuta, who is incredibly cold, harsh, blunt and obsessed with perfection. There is certainly a bit more to him, but I think that's a bit of a spoiler and... I don't have much to discuss about that aspect of his personality so I don't feel like adding a tag for it...~

#####Classic glasses guy pose

They also briefly introduce the other three bands at the end but it's so brief it doesn't really matter. Like seriously they don't even get animated in 3D, if they even physically appeared at all, they had such a minor role.

Overall:
It's a brilliant and emotional story. It's got a couple funny moments and some heart-warming ones, exciting moments and some sad ones, paired with brilliant inserts and some pretty good characters~ It's got everything you'd want in a show of its genres and does it all pretty well, though it's far from the best.

The first three episodes might not be great and it takes a while to truly pick up afterwards... but when it does it is really amazing. Episode 8 has the best music, then episodes 9 and 10 have such brilliant emotions– it really does become amazing there~

Please, just try it~ It'll make Ryo happy too~! ~~I think. Probably.~~

#####*Oh Ryo you have no idea how happy I was when you finally said something like that in the fourth freakin' episode you appear in...~*