I'm a big longtime fan of the anime, who did not go into this expecting a 1:1 recreation, and I've gotta say, I'm floored. I loved it. Here's a list of directors (and movies) that the live-action reminded me of in terms of cinematography, direction, acting, prop/costume/set design, atmosphere, and narrative:
-Dick Tracy (Julia's narrative reminded me of Madonna's character, and the atmosphere/stunt choreography reminded me of the approach that movie took. Also, some of the character design, especially the weirder faces of some characters, with features that have obviously been exaggerated with makeup)
-Robert Rodriguez (scenes that employ action and dialogue fluidly and simultaneously. The dialogue may not be as nuanced, and almost Tarantinoesque by comparison. Lastly, I'll make the Rodriguez comparison due to the gore factor, which is more present in the remake)
-Kill Bill (since I brought up Tarantino, it can't be ignored that there are parallels in the approach to exposition and dialogue, as well as some of the action sequences, with one scene in particular being very reminiscent of a scene from Kill Bill)
-Terry Gilliam (movies like Brazil in terms of set design, and the way Gilliam leans into the absurdity of things and conveys that through the almost fragile appearance of props, sets, and even actors at times)
-Hitchhikers Guide (lighthearted approach to narrative, set design, visual effects)
-Taika Waititi (Thor: Ragnarok to be specific, in terms of the non-serious approach that was taken with regard to prop/costume/set design. Always giving the viewer something to look at, and depicting a world in which old and new tech exist side by side)
-Star Wars (I can't not make this comparison, as anything live action that takes place in a world with space travel inherently owes some of its use of special/visual effects to the original trilogy)
-Fifth Element (very similar, and again, non-serious approach to prop/costume/set design)
-Scott Pilgrim (similar approach to the depiction of action sequences. Maybe not what all fans wanted, but certainly not something there wasn't an established precedent for in this medium)
-David Lynch (in the sort of "dark soap opera" quality of the Viscious/Julia scenes. I loved the Viscious plotline, and thought the way it weaved in and out of the main narrative was similar to the way some characters are periodically revisited in Twin Peaks, or the relationships of characters in Blue Velvet. It feels intimate and secluded from the action everyone else is a part of, while the characters in that space are vulnerable and unsettled)
Lots to love for the show here, and that's because it didn't try to do the same thing. I prefer that it took its own approach, and I think more creators should take risks. If you don't like it, sorry I guess?