My order from best to worst is 1, 2 and then 3.
The gap between 1 and 2 is pretty small for me but the intimacy of the world in the first game is unlike anything I have experienced before, even to this day. It's hard to explain this but the world feels 'real'. You can feel the love put into almost every NPC, who don't just feel like they are inserted into the world for the sake of it. For example, look at how the relationship between Kurita san and the flower shop girl develops as the game progresses, or how the guy working night shifts at the tomato mart's problems slowly begin to escalate to the point that he has to work a job at the harbor. In the first game, there is so much attention to detail and you are rewarded for investing in its world and talking to people. I love how these things, along with the events in Shenmue 2 and the conversations with Joy, are left to be organically discovered, rather than being guided towards them via plinking icons as you probably would in Shenmue 3 as a result of the new sidequest system. The first two games (but especially Shenmue 1) are more of an 'experience' than a game. The generic RPG elements brought into Shenmue 3 kill not only the sense of reward you get from randomly initiating an event but also reduce the merits of exploration and engagement with NPCs. Most NPCs aren't worth talking to in 3 (for non story related reasons) unless they have the sidequest icon next to them, as this is often the way in which they get some form of 'development'. The exception to this rule being the reactions post Ryo's encounters with the thugs. My main gripe is that I'm constantly being reminded that I'm playing a game in Shenmue 3 (which sounds weird because I know that's what it is) but the first two in the series never made me felt like that. They fully pull me into the world.
While Bailu can be charming and feels mostly like a Shenmue game, it still doesn't fully capture essence of the originals. It's a poor man's Dobuita for me (but still enjoyable). Niawou and the castle part of the game are a stain on the series and I don't think it would be fair to even say that side of the game is a 'poor man's Hong Kong'. Overall, a lot of the new changes to Shenmue 3 involved introducing generic RPG elements into the series (stamina/food system, Yakuza-style sidequests, etc) which has served to steal away some of the charm away that the originals exuded. That being said, I don't think 3 was a terrible game and indeed, I feel with some additional development for Niao Sun, Ge, broom girl, Ren, Shenhua (in Niawou) and fat guy, along with a less-rushed ending, it could have been very enjoyable. Because of this, I still want a fourth game as much as I did a third, because I'm optimistic that Yu will respond to our feedback, implement it and deliver a great sequel.