More or less true, but it also focuses more on how they got where they are at the point of the story, whereas Brotherhood I think already assumes you saw the original so it throws you in the deep end more, a bit further into the story and then has some flashbacks; but they're not as impactful (IMO) as the original anime managed. Watching both gives you the context and probably a bit more emotional investment going into what Brotherhood presents
Also if you like Hard Sci-Fi as opposed to more fantastical Sci-Fi, you may really enjoy Planetes [Debris collection..., honestly doesnt sound exciting, but watch it, its fantastic and a lot of real science in it]
Mecha also often leans hard into full Scifi, I'd recommend Full Metal Panic as a good entry into that genre, as it isnt as serious, and at least one of the series (Fumoffu) is a full blown fish-out-of-water comedy; and the last series made for it was actually only released a few years ago. I kinda hope they make more.
If you don't mind older anime, Banner of the Stars was great (full sci-fi drama), and although I've never got around to watching it Legend of the Galactic Heroes always comes strongly recommended.
Steins Gate is worth a watch, Cowboy Bebop, Gurren Lagaan also. Gundam/Macross are almost thier own entire genre adjacent to mecha at this point.
Parasyte. For SURE Ghost in the Shell.
Knights of Sidonia maybe too, although I dont like the CGI animation style.
Edit: Sorry added a lot more here as my mind wandered back into the past, I've not had time to watch as much in more recent years.