After chapter 3 I think I've played enough to make a short-term impression of this game (Iv'e got other shit to play). It's a functional stealth game that even manages to do some pretty cool things, but from a structural standpoint, it isn't Thief.
It's a lot like the difference between the original Crysis and its sequels. The original game is an objective-based affair where the missions are working, dynamic environments that react to player choice. The new game is a string of small stealth arenas that are cleverly designed, if sort of tiny. The old game asked you to figure out out to infiltrate generally open-ended environments. The new game just asks you to reach then ext waypoint. Based on just that, most people who are actually wiling to play a stealth game should probably enjoy this, but it certainly won't satisfy those who miss the more simulation-oriented games. Dishonored definitely comes closer to accomplishing that. Does this game offer a lot that Dishonored doesn't? I don't know, I guess the lack of super powers depending on how you play. Choosing to play Dishonored without superpowers in my opinion actually makes for a better Thief game than this one.
I do like the first person body experience in new THIEF though. It's a sensible evolution of how Thief and Thief II displayed Garrett's movement onscreen. In those games Garrett's feet were already visible, and every step you took was pronounced with an audible sound and a head bob. Actually animating Garrett's hands with every action enhances that sense of feedback with every thieving action you make and doesn't really intrude on the gameplay.
Also, thematically this game is actually surprisingly faithful to The Dark Project despite rebooting the setting and removing the Hammerites, Keepers, and Pagans. Most of the same themes are there: conflict between nature and technological progress, progressives messing with ancient forces beyond their understanding, etc. Chapter 3 is pretty much a straight callback to a Thief Gold mission. Garrett in the new game is doing pretty much the same things he did in the old games.
Voice acting is quite uneven in my opinion. Characters like Garrett and Basso work, but others not so much. NPCs accents are also all over the place. A few sound like they just grabbed local Quebec voice actors, some sound British, and some seem to use Britishisms with an American accent. They don't have to stick to the old games (where everyone had an American accent with the universe's own jargon) but they should have just picked one.
Visually, I'll say again that it really shouldn't have been released on PS3 and 360. The game works, but you can tell that visually it's a PS4/Xbox One/PC game that had its textures and effects ripped away for the PS3 and 360 conversion, where usually most early next-gen games are the other way around. One of the biggest signs of this from what I can see is that the shadows have just been destroyed. Shadow edges on PS3 show off pixelation reminiscent of PS1 games. It also magnifies the general lack of color I see in every version of the game.