I'm gonna choose Arkhamverse Joker, while it's heavily implied (if not outright stated) that he did suffer one bad day (with references to the Killing Joke), it doesn't really seem to completely effect him unlike Nolanverse Joker who at least is implied to have suffered something akin to losing soldier comrades which gave him PTSD.
Not to mention, there's implications that Arkhamverse Joker's reason for his malevolence was more out of a selfish and egotistical desire to get attention which invalidates any tragic past he might have had. (Nolanverse Joker is also far past any tragedy he might have had but Arkhamverse Joker invalidates it much more)