Café de Nuit

I was inspired when reading a Batman comic for a domain, add in some Sherlock Holmes and Victorian England and you have a setting.

A city has been infested with crime and poverty, government corruption and a privilege elite falling to vices. A hero rose from the shadows, a masked vigilante fighting back against the dark. (Basically batman, but different)
At the same time rose a criminal mastermind, someone with daring and flair to upset the status quo, with a disregard for conventional society.(our darklord, is basically the joker with some Moriarty in there) the vigilante stops some of our dark lords crimes and they become rivals, the criminal feeling a kindred spirit in him, like someone understands now. Our dark lord develops a love/hate obsession with the vigilante, as they become more unhinged, there world view more twisted, descending in to madness. He became more deprived and deranged in his obsession. In a major confrontation with his foe, it was all laid out, how they are the same, how they need each other, how the world is mad. The hero rejects it all, saying they are insane and just want the world to burn. The dark lord loses any restraint they have in the fight and they both go out a window. The mists rise as they fall, the dark lord awakes in a safe house hurt but healing.
The dark lords torment is to never be understood, to be rejected, that his world view is warped, that he became a monster because he had the capacity to be a monster and it was easier than healing. The vigilante has other foes that challenge him

You could also switch it up, and have the Batman stand in be the dark lord.

He’s so obsessed with keeping people safe that one day he snapped and burned down the Arkham Asylum analogue in his world, killing all the inmates.

He gets pulled into the Mists and his curse is his city will never be free from crime and danger. Every time he kills a villain, another one pops up to take its place, each one with a different power that means any tactics he learnt against the last are pointless.

There's also the possibility that both of them are co-darklords, both corrupt, both delusional and obsessive- Victor Mordenheim/Adam sets precedent in that regard.

More thematicly though...what if the Joker analogue fell into Darklordship, and the Batman analogue, while somewhat flawed himself, did not-rather, the latter chased him in attempting to save him. The Darklords, naturally, use the latter (and his slowly growing vigilante family) as the former's eternal torment.

And Our Vigilantes, battling Darkness but not succumbing, often hold out the possibility of rehabilitation, only for the madman obsessively refusing. Endless entertainment for the Dark Powers...