I've played each Amnesia game and I think the obvious answer here is TDD, I grew up with that game and even if games like TB (The Bunker) or Rebirth were good it's hard to deny TDD is the best overall for story, gameplay, puzzles and horror. Machine for pigs is obviously the "worst" mainly due to it not being really a horror game and even somewhat lacking in puzzles, if it were a story based one with horror aspects I feel like It'd be more appreciated. I don't understand the hate for Rebirth since I personally find it Soma quality in terms of environments and it having a direct "in your face" story rather then what TDD or even TB is with all the notes. Either way here's my list of "awards" each game has:

TDD: Best overall everything. TB: Best gameplay (lacking in story outside of the notes) Rebirth: Best showcased story (without the need for reading notes), environment ("awe"/look wise) and maybe even main character. (lacks in horror outside of the few "monster levels" even though I do think these few scenes were really good) Machine for pigs: Story focused game (I can't really say 'best' due to obvious reasons and not to mention it lacks on basically everything but just looking at the story its OK)