I just don't get how something from the 80s can look so much better than something from 2018
"Better" is subjective. It looks fine to me; it's simply a different, more cartoony aesthetic. Animated shows in the '70s and '80s tended to have a pretty standardized look; comedy shows could go more for caricature, but straight adventure shows tended to use a consistent, naturalistic style. But that divide went out the window when
Batman: The Animated Series embraced cartooniness and caricature and made it work in a very serious, dark, mature show. And animation character designers over the past 30 years have continued to innovate, giving each show its own distinct, individualized design style. Obvious not every single show's style is going to appeal equally to every individual's tastes, but it's hardly valid to say that the vastly greater creativity and experimentation of modern animation designers is "worse" than the rather limited, uniform character design aesthetics of the past.
There's also the fact that this
She-Ra is far more of a comedy than the original was, so the more cartoony look is appropriate. It's not that great a departure from the character designs of other Dreamworks Animation shows like
Voltron: Legendary Defender and
Dreamworks Dragons, shows that also blend comedy and adventure. There's an anime influence too, which fits pretty well with the nuanced character writing and ambiguous villains. (I saw a headline suggesting that the Adora-Catra relationship is very similar to a core character arc in
Naruto, though I'm not familiar with that show.) As I've remarked before, what's surprising is how little of Noelle Stevenson's characteristic cartooning style is evident in this show, although I can see a hint of it. It's basically a cross between Stevenson's aesthetic, a
Sailor Moon-type anime look, and the Dreamworks "house style."
One way in which the character designs are definitely better is the range of body types. All the women in the original
She-Ra had the exact same Barbie-doll figure, a requirement of the toy designers so they could use the same body molds for all the dolls and let them exchange clothing. (Probably made things easier for the animators too, since Filmation liked to trace the same movement sequences for multiple characters.) Here, we've got a much more inclusive world with women and girls of many different body types as well as different ethnicities.