Something that needs to be said about this series before anything else: this is not a remake, it is another adaptation of the book series by Yoshiki Tanaka. That needs to be said because it is not seeking to be a remake, and referring to it as such, and making the due evaluations, is simply incorrect. It must be considered its own separate work, independent of the old. With that said...
"Legend of the Galactic Heroes" is, of course, considered a classic, and rightfully so, with its expansive, and intriguing cast of characters, its high stakes story, intelligent and sometimes provocative themes and discussions, and a setting that suits everything. It's left its mark on the science fiction genre, and I'd be surprised if a number of other anime didn't take influence from this one. The new series I hear was in development for a while, and it obviously had quite the shadow to escape? Does it succeed?
(I'll do my best to judge this series on its own merits, but comparisons will be inevitably drawn to the original)
Story: 5/10
Having finally read the book it was based on, I can safely say that this series is a more faithful adaptation of it. The original series added a few additional scenes, as well as expanding on existing ones. This series follows the book quite closely, and mostly expanding on scenes within those parameters (such as showing scenes that the book references, but doesn't dwell on). But that said, does it automatically mean the story is better? No, not by any means.
Sadly, while the story isn't bad necessarily (it still gets the plot down, and the characters motivations are established), the original took the time to very firmly set up the setting, and how its influencing the characters. This series is far more faster paced, and is dedicated primarily to moving from one plot point to the next. Not as much time is spent dwelling on the build up and fall out of what happens. To that end, some of the dilemmas and personal conflicts get nudged aside. It does the story a great disservice.
Art: 9/10
The animation and action in this story is amazing, some of the best I've seen in a science fiction anime. In many respects, this is what I feel the original could've been if it had the technology we have now. The space battles are quick paced, flashy, and appropriate grand in scale. I especially like the design of the spaceships.
Sound: 8/10
While the original favored classical symphonies for their soundtrack (which favored the setting quite well), this one favors faster music with. But that said, I personally really liked the soundtrack, especially the opening, "Binary Star".
Character: 6/10
As I touched upon in the story section, the series doesn't spend as much time dwelling on the motivations of the characters as the original does. Unfortunately, that means we don't get much beyond their base. This would've been a "5", if not for the series still managing to get the characters motivations and base traits correct, which is probably the most important part. Its enough to keep attention, not enough to really suck one in.
Enjoyment: 7/10
What sells this series for me is its action and animation. As a big fan of the space opera genre, I enjoy anything of this scale and concept. However the story moved too fast for my taste (and I usually prefer fast pace stories), and didn't give the characters the all important time to flesh out fully. But I tried to enjoy it for what it was instead of what I wanted it to be.
Overall: 7/10
If one can get past the original (which I understand is very hard), there is some stuff to enjoy here. But don't come in expecting the original, because that's not what you're going to get. It can be seen on Crunchyroll, so maybe give it a try if you have some spare time and make up your own minds.