I liked season 1. It's sober and realistic, but also very good. Season 2 is the same and well worth watching, except that I'd say it's slightly weaker because quite a lot of it has the main character (Kumiko Oumae) just watching other people's emotional crises. The show used to be stronger when its stories were built around her. However these background story arcs are still very well done, while the concluding run of episodes makes things personal again with Kumiko, Reina and Asuka.
It's interesting to compare it with K-On!, which I hadn't watched when I saw Season 1. Both are Kyoto Animation shows about music-playing schoolgirls, but I think their plan here was to make the anti-K-On!. That show is bubbly, slice-of-life fun with four airheads who goof off and eat cake. Sound! Euphonium's message, on the other hand, is that success comes from lots of hard, unglamorous work. Kumiko Oumae and her friends have to earn their victories, which aren't guaranteed to involve gold medals. Happy endings aren't automatic. Love is unlikely to be requited. Parents and families can be horrible (or dead). There's a discussion about whether competitions are just a cruel way of inflicting pain and pressure on people. People can make bad choices, then spend years regretting them. All that is the opposite of escapism, but fortunately this is also a kind, sensitive show and I always enjoyed it.
Note, for instance, the title sequence. There's a shot of four girls pulling a cool anime pose (badly), but it's followed by another of them laughing at themselves afterwards. The key note is realism.
The show's relationship stuff is fundamental, but also so understated that you'll miss it if you're only following the dialogue. It's a Kyoto Animation show. You've got to give it more attention than most anime, because the animated characters' acting has more subtlety and layers. It's in the body language and the ambiguities. Look at the shoelace-tying in ep.6, for instance, which is so sledgehammer-like that it's bewildering and yet is also a wordless throwaway that only lasts a second and wouldn't even be detectible in a simple script transcript. Similarly, "I love you" and "I like you" are the same sentence in Japanese and it's sometimes hard to know which was intended. The last couple of episodes contain three such "love" confessions, but one of them is misunderstood when you'd think that had to be impossible and the other two are so ambiguous that you could show them to two viewers and get three interpretations. Look at Asuka, for instance. She flirts so shamelessly with certain particular girls that I started wondering if her jokes might perhaps have been intended literally, hidden in plain sight under the fact that Asuka's a cynical, flippant tease who'll say anything and seems to take nothing seriously.
Note also the comparisons between Asuka's and Kumiko's older sister. There's more to her than maybe-relationships, daddy issues and a monstrous mother.
It's very good. I admire it... but at the end of the day Yoroizuka's being a bit silly, Kumiko's sister's story has only an indirect dramatic impact and even the other characters eventually start discussing whether or not all Kumiko ever does is watch. (I'm not saying Yoroizuka's problems aren't realistic. There are indeed such people. She's in pain. However it is also all a bit silly.)
I still like it, though. The last few episodes made me properly enthusiastic about it again. The conclusion is delicate, ambiguous and nice. It's an anime to recommend to people who say they don't like anime.