The term epic is way overused by people nowadays but under the dictionary definition "noting or pertaining to a long poetic composition, usually centered upon a hero, in which a series of great achievements or events is narrated in elevated style" it fits in this instance. Legend of the Galactic Heroes is epic.
LOTGH is an adult anime, not for sex or language, but because it was not made with overreacting characters whose eyes bug out or the characters whole color change. It is mature and well thought out with no child like gimmicks. Those used to regular loud and obnoxious animes may find this boring by comparison.
The scope of it is truly huge, with battle fleets of 20,000+ ships and citizens numbering 20,000,000,000+ under one regime. They show you not only the main characters and their back stories, but the tactics used in massive fleet battles and the politics involved in such massive empires.
I've watched the first two seasons multiple times and impatiently awaited season 3 from Funimation. I just recently checked and saw it was available so I'm rewatching season 1 and 2, that way I'm fresh on everything before eagerly heading into number 3.
I haven't watched the original as I was unable able to locate an English dub so I can't comment on how closely it follows the original. But as far as a standalone show is concerned it is 'epic'.