Both versions, on the 'flix.
The live-action one looks good, and visually the actors are close enough to the anime I don't mind much. Spike (John Cho) is cool, but stiff, and his kung fu is clearly done in CGI on a ragdoll in many scenes. Jet (Mustafa Shakir) is much better, occasionally rises to actually funny. Faye (Daniella Pineda) has a cameo and she's all right, but we'll have to see her for longer. Anyone demanding Ed or the dog right now is an idiot, they don't show up until later if this show follows the anime at all.
The ship looks great, nice analog switches and crappy machines that don't work without thumping. It's not quite as bric-a-brac random parts as the original, but maybe looks more functional. Spike's plane is much, much better than the anime's, it actually stays the same size in every shot, looks like it works, it's not just a badly-drawn plastic toy. So +1 there.
The habitats are just planets, it seems; you don't really get a sense of them putting up a dome on a barren rock. Obviously it's hard to be on the ground and show this, but we have CGI where you can paste a real thing onto an animated asteroid, and they don't.
My hearing is aging badly (Mark pauses to bat at his ear and dig some wax out), because the jazz is far less annoying than it was when I first watched this. If you get old enough, even terrible incoherent noise becomes tolerable! Sorry, jazz fans, but you're wrong.
So for comparison, I watched a couple eps of live-action, and a couple eps of anime; haven't seen those in 20 years.
The anime kung fu is only a little more cartoony than live-action's, and it's of course believable since they're cartoons. What seems dumb live, is fine animated. There's often more text & backstory setup in the anime missions. If you pause video, you can see the fight scene restaurant on TJ habitat was established in 2025! Uh, we're not on schedule for that. Also, the Moon blows up in 2021, so we still got a few weeks for that to happen. The habitats are definitely just one power-failure away from everyone dying, they look ramshackle and barely fit for survival, which fits with the setting.
When I made fun of Spike's plane above, I wasn't overstating it. It looks so trashy in the anime, it deserves a special Golden Raspberry award for unspecial effects in a cartoon. It'll go from so big it can't roll out of the hanger without folded wings, to small enough to dash down a highway through power lines, to big enough to catch a falling object on, in the course of a single episode. One scene, Spike stands next to it and it towers over him. Another scene, he's got his elbow on the windshield and feet on the ground.
The Tijuana job is almost the same between them, and the live-action show fills out Katerina's backstory into something interesting, has a much more plausible meet-cute with Spike, the guys aren't on top of "Asimov" (why? all names mean something, and this guy's no cold rational robot writer; did they know how much of a womanizer and ass-grabber Isaac was? It doesn't make sense even ironically). The Syndicate is a much earlier, more serious threat in the live-action show. They're just random bozos for a long time in the anime. Even when the ending's the same, it's 100% better in the live-action because she has a motive.
Overall, I like the pacing of the live-action show better, I'd prefer a bit more setup, but they're weaving the plots in far more subtly than the jumpy, twitchy anime did. They really should've got someone taller and more fit to be Spike. Andrew Koji's busy doing Warrior, but there's like a million other slightly younger guys with actual kung fu experience who could've done it.
In any case, it's a… not hard SF, but not complete space fantasy… with decent production values and a lot of fights. You can't expect The Expanse every week, right?