As someone who hasn't watched the original Yamato series from the seventies, I cannot compare the two. However, it is easy to see that quite a few things were kept the same, even though they now appear outdated.
The premise and general setup are typical for a soft SciFi space opera: After evil aliens have attacked and devastated Earth, the Space Battleship Yamato must leave on its great voyage to the faraway Iscandar to retrieve a device that will return Earth to its former beauty.
The SciFi part itself is fairly soft, not too dissimilar from, say, Star Wars. There's a magical gizmo that allows FTL travel, artificial gravity is an unexplained thing, and occasionally the dialogue mentions a technical term (like 'interstellar medium') that the writers have no idea about. That's pretty much par for the course for almost every SciFi show, but still something that should be easier to avoid now that one can look things up on the internet.
The Yamato and spaceships in general have a charming naval theme going on, where destroyed ships are called 'sunk' and dimensional submarines are a thing and fighter carriers look quite a bit like aircraft carriers. It's a bit silly but works very well.
What definitely has been stuck in the seventies are some gender-specific thing. I'm not really someone who notices these things but, uhh, when the men wear sailors' uniforms and the women skintight, high-heeled bodysuits, it's a bit on the nose. It doesn't help the primary female character regularly plays the damsel in distress, and even the secondary female character (who is quite kickass most of the time) runs away in tears when she sees her crush talking to another woman.
Generally, the characters were a bit forgettable to me, though that's likely due to the amount of them. The Yamato's important crew is comparable in size to that of various other space shows (think the various Star Treks or Battlestar Galactica), but with only 25 minute segments it's a bit difficult to give all of them enough screentime. Still, by the end of the show, I felt for most of the characters. There're some pretty cool antagonists and occasional side characters, too.
The plot... mhh. As said before, it's typical space opera fare that must've seemed new and daring in the seventies. Today, we're just used to other stuff. To be honest, it's almost campy at times: the evil aliens are basically space nazis that look like humans with blue skin. The good aliens are beautiful blonde women that look so much like humans that they even get confused. The wildest thing you'll see is someone with greyish skin and pointy ears, so... But still, the story works out. I didn't much like the first few episodes; they felt a bit bland to me and I hadn't yet liked the characters. I'd say that the story turns for the better in episode ten, and the last ten or so episodes are absolutely marvellous. If it were only for the first half of the show, I'd give it a 7 at most, but in total it's definitely worth an 8.
As for the production values, the soundtrack is fairly good but gets repetitive. If you binge this series, you'll probably get sick of the same five themes repeating ad absurdum but in small doses they're very catchy. The graphics are fantastic: a perfect blend of CGI and traditional cel animation. The (Japanese) voice acting is solid as always. I'd say the direction and editing is nothing to write home about, but I'm not really someone who notices that stuff.
Also, perhaps important to note is that there is pretty much no fanservice, so you can safely watch this with your kids or parents or whomever.
