From my least to most favourite...
I... really do NOT like Dark Souls 2, I dislike a lot of the way they changed Humanity and the way that functioned in terms of online play and the levels, bosses (Old Iron King), themes, and story are easily the laziest in the series. The game lacks any of the magnificent thematic oomph that the other games had.
Demons Souls comes next, it's amazing and it's the first, it's still beautiful and haunting and has some amazing themes of its own (the source of magic and miracles) but it has some really weird ideas in it because it was the first one (world tendency, how impossible it is to get some upgrade materials, etc). It's still right up in my top 25 games, the only reason it's here is because the other three are exceptional.
Now, the last three are within an hair of one another in my opinion, but, I'm going to put Bloodborne here because, despite the early levels capturing that feel of interconnectedness from DS1, and the INCREDIBLE aesthetics in here, either a filthy, diseased look reminiscent of art from the Black Death, or dark, foreboding gothic horror, to the transition we get into the otherworldly lovecraftian aesthetic and how the world changes as you gain more and more 'insight'. Some of the "dream within a dream WwooooooOOOoooo" style elements piss me off because it just doesn't give anything grounding, it's a 13 year old's idea of "deep and mysterious". Furthermore, the NPCs in that game are the flat out worst in the series, they do one thing, maybe do it again another time, then they die. Aside from those gripes, the mechanics, and the levels, and the bosses are just amazing.
Out of these last two... Damnit, I have to dive Dark Souls this spot... I adore this game, it's in my top 5 games of all time, but the later levels like Izalith and reused elements from Demons that don't quite work just mean it doesn't make the cut... But, if you ask me to ever recommend a Souls game to someone, it's going to be this one because it's the quitisential experience of the series and the later games are only improved by playing this one first, while this game needs you to go into it fresh and discover the world for yourself. The only thing that REALLY holds this game back is places like Izalith which are just a chore to do every time and BONEWHEEL SKELETONS! [http://i3.kym-cdn.com/photos/images/original/000/608/139/975.jpg]
So, by process of elimination... Dark Souls 3 is my favourite but only by a gnat's whisker. It's the game with the most consistent quality, it writes the horrible Dark Souls 2 mostly out of the story, it's a little to big on calling back to Dark Souls in places but From Software have always reused designs and assets (even Seath in DS1 was a reused design from one of their Kings Field titles) so I can overlook that because they seem to try and make things different enough. The combat has some issues, miracles and magic are nerfed and the change from Poise to the Hyper Armour system causes issues with certain kinds of armour and the builds around those. Still, it's the game that brings elements from EVERY previous game, from the increased speed and amazing boss designs of Bloodborne, to the magnificent hub space from Demons Souls, to the increased ring and weapon equip slots and flexibility from Dark Souls 2, to the atmosphere and feel of Dark Souls, it takes a little bit from every game and then adds its own, new mechanics that make it its own game. I think the story is a little too much like DS1 but I do still enjoy it and it gives us the NPC stories in the world that make the series really stand out more than anything else.
Please note, I did not count DLC in this list, if I did, Dark Souls would beat 3 hands down, Artorias Of The Abyss is AMAZING and Artorias himself is my single favourite fight of the series. The painting we get with Dark Souls 3 is interesting but lacks the same sheer brilliance that tied AOTA magnificently into the tone and themes of the first game.