"Arthur has a quick draw" When the **** has this been a thing.
All he did was pull a gun on a middle-aged dude who was sitting on a chair carelessly and who wasn't expecting him to shoot. It doesn't count in the slightest. And his draw wasn't quick, he pulled it at fairly normal human speeds.
Meanwhile Killing Joke Joker has... Again, better equipment (Explosives, more varied guns, Joker Gas), but he's also a better fighter and much more durable (Endures a brutal beatdown from Batman), and more intelligent, being a professional and experienced criminal and not just a guy with a grudge on society.