Freddy vs. The Joker, this I know is completely hypothetical and there are many variables that would make this an easy battle for Krueger. The fact is, Freddy is already dead and wields a power of demon-like sorts. He could basically just end his victims whenever he sees fit. Let us forget all of that for now and focus on the fact that even though Freddy could just kill his victims, he has a knack for wanting to toy with them in their dreams to induce fear. As we find out later in Freddy movies, fear is the source of his power.
Freddy Krueger, a serial killer of children, was captured by authorities but released due to a technicality during trial. Krueger was later hunted down by an angry mob led by his victims' families. He was cornered in a boiler room where he used to take his victims and then the building was then set on fire with Krueger inside. He was burned to death. His body died, but his spirit returned.
Krueger returned from the dead with his burned and disfigured look, wielding a glove with razors on his right hand, to kill his victims. Freddy chooses to attack his victims through their dreams, where he has total power and dominion. Most of Krueger's victims are teenagers who fall asleep and end up becoming part of Freddy's funhouse of torture. As he toys with them, he produces as much fear as possible, before finally ending the game.
Now we have Christopher Nolan's Joker. Though we know little about his past in The Dark Knight. We know that he's a crazy sociopath. (Even though he claims not to be.)
Heath Ledger once told The New York Times he viewed his character as a psychopathic, mass murdering, schizophrenic clown with zero empathy. The Joker doesn't even care about himself. We know little about the origins of the Joker throughout the Dark Knight. He often speaks the line "Do you wanna know how I got these scars?" during the film, however the story he gives changes every time, offering very little insight into his past, so no one truly knows his beginnings.
The question we are asking here today is: How would the evil master of dreams fare, if he were to have found himself in the mind of the Joker?
I believe Kruger would be in for a world of surprise if he wandered into the mind of this individual, who admittedly states he is an agent of chaos.
Who would win in the game of wits? Both thrive on the same principles, yet Joker seems to have far too many other issues that would take things up a level for Krueger, giving him some serious troubles in seducing fear from the Joker.
In the end, I believe Krueger would have a real problem making The Joker fear him, even using Batman as a scare tactic. This could possibly frustrate, maybe even weaken Freddy which would give the Joker a chance at dragging him into the real world, where Krueger is a vulnerable as a human.