TL;DR: the Legend of the Galactic Heroes is a great anime in its own way: it’s well written and well produced, especially for its time. But for most people, it is either a slog or too abstract to enjoy.
Synopsis: in a distant future, two factions fight for control of the stars: the Monarchic Galactic Empire and the Democratic Free Planets Alliance. Within these factions, the series primarily follows two military commanders who begin to rise through the ranks of their respective militaries.
Within elite circles, Legend of the Galactic Heroes is probably the anime that is considered to be the best. It’s not — that title goes to one of the big 5: Fullmetal Alchemist, Death Note, Evangelion, Berserk, and Steins;Gate.
As for why this series has risen to the status of the most acclaimed anime ever, some of it is due to just being good, and the rest is because people recognize that the people who like it tend to be high status, so they either pretend to have watched it or psyche themselves into thinking they enjoy watching more than they actually do.
I did, in fact, watch Legend of the Galactic Heroes. And, to be honest, I didn’t like it. It was too slow paced and dialogue heavy; it didn’t matter how good it was otherwise because those two elements alone were sufficient for an unenjoyable experience.
Legend of the Galactic Heroes is indeed a well-written anime: there’s a giant cast of characters with explored backstories and dimensional personalities. Nothing happens in it that seems extraordinarily unlikely or unrealistic. It was predictable in the grand sense, because everything happened as it should but the way the grand events unfolded was not.
It’s art (notably character designs and backgrounds) are underrated and aged well:
The voice acting was also solid and the studio chose actors to suit the ages, builds, and faces of the characters; Reinhard in particular had a well-suited voice actor. Most of the soundtrack is classical music; personally I’m not into that genre of music so I cannot speak as to its quality, but it sounded fine for the most part. I didn’t have a taste for their openings and endings, except for this one, that was fantastic:
There was basically no action in this anime, and the little that there was… Kind of sucked.
In the grand scheme of things, it is not a big deal, as nobody watches LOGH for the action.
I still think Cowboy Bebop is the best Anime ever but it has some of my favorite music ever so idk.
LOGH was really really good until Reinhard won the Galactic war. Then it got a little contrived and lame imho.