Sure, DSIII has 100s of different build possibilities to experiment with, but Bloodborne ditched all that fluff for a few completely unique ones.
To me, the latter results in a more fun and focused game.
Speaking of combat. Ditching shields for parry-focused firearms, fast side step dodges as well as rolling, trick weapons, health regain system that promotes getting back into action as soon as possible... all just cement it as the best Soulsborne game in terms of gameplay.
Now speaking of the story, world and lore within it... DSIII is interesting, but Bloodborne is just beautiful lovecraftian insanity. There's much more to it than the entire Dark Souls trilogy combined... just check the books written about the intrecacies of its lore. From did an excellent job adding their own twist to cosmic horror.
Music...
Dark Souls III has a few memorable tracks but is mostly Sakuraba-style stuff. Bloodborne has one of the best, high quality/production OSTs of this gen.
Then comes monster/boss design. Little details like when you find eyes in pots/jars in Byrgenwerth, how the Shadows of Yharnam fade in from the shadows which is perfrctly fitting of their name, how in the nightmare of mensis stuff gets really weird like dogs with crow heads and vice versa, how the more insight you collect the more you literally hear and see of the world... and that's just a very small sample of all the attention to detail and atmosphere building in the game.
All in all, Dark Souls 3 is a great game that I enjoyed immensely, but it relied a bit on Dark Souls 1 nostalgia and didn't feel like a truly fresh new experience. Its combat was faster, but coming after Bloodborne that speed increase couldn't be fully appreciated. In the end, it is a great game but Bloodborne is an all time masterpiece.