Can anyone name a Joker story from Moore that's not TKJ? They both wrote one Joker story back in the day.

And while TKJ is (for better or worse) pretty much the definitive Joker story, I'd actually say that Miller "won" the debate if we're going to look at what followed. Aside from a few isolated stories, the modern take tends to be Joker-as-supreme-mass-murderer, which owes way more to Miller than to Moore.