I read the article about Freddy versus the Joker this morning. As someone who has experienced a degree of psychosis I have a lot of experience examining not just the conscience mind, but the deeper roots of psychopathy at a deeper level than most at an esoteric level.
In this case, I am going to give ultimate victory to the Joker and here is why:
Freddy draws his power from fear. For that to happen, his victims have to be capable of feeling ultimately helpless. They have to feel like this is hell and there is no way out. The truest forms of victimhood are found in this concept.
Freddy feels like he, himself, is a victim. He killed children, likely because he felt alone and resented the world. At a deeper level, perhaps he resented their youth which would lead you to believe that his childhood wasn't great. Given origins as the product of repeated rape, it is easy to imagine that he was ostracized and teased for the trauma his entire life.
In the end, Freddy was born from suffering and died suffering. Therefore his lot as a vengeful spirit is to torment others.
This is a problem with the Joker. The Joker too, has no doubt suffered horrifically. So much so that he never gives a straight answer as to who he really is or where he is from. The key difference here is that the Joker has transmuted his suffering into a type of anarchistic madness. The Joker is extremely intelligent and has mastered the art of staying ten steps ahead.
The Joker has excepted that everyone suffers. Everyone is, just as himself, corruptible. Freddy is already far gone into that corruption and has in fact made it his life... And his death.
Seeing this the Joker would see opportunity. He would pretend to play the victim at first, but it would be a ploy and Freddy is clever, but not terribly bright. Most of his ideas come from the minds of his victims.
That being said. He wouldn't know what to make of the mind of the Joker. In the universe 52 in DC comics, the Joker cuts off his own face and wears it as a mask. In one issue The Joker chains up his own sidekick in a room full of skeletons dressed just like her and tells her that she will rot to death there.
Needless to say, Freddy has never encountered someone crazier than himself and that fact alone would throw him through a loop. In the end, I believe that the Joker would find a way to use Freddy to his own ends by the process of manipulation and charismatic psychosis. Freddy would end up being used against Gotham with the Joker pulling the strings.