I only found out about the story of Jeff the Killer today, and after reading the story, especially the descriptions of his appearance, I can easily see why he is considered a ripoff, or to put it more gently, at least "inspired" by the Joker character.
Since I only found the story today, the only resource I have found giving me clues as to when this story was created was from knowyourmeme.
Pale skin is nothing new (especially where horror is concerned) but white skin brought about by a chemical fusion was Joker’s before it was Jeff’s, as well as the self-mutilation of creating a smile in "The Dark Knight" which (according to the only source I could find) was released about half a year before Jeff the Killer even began to get off the ground. The hair is kind of a moot point, since green hair gives Joker more of an identity, and is not necessary, nor encouraged, to be implemented on Jeff. The only things left setting them apart is the burned eyelids/leathery skin which has been in many things, but at least wasn't applicable to the Joker, unless my Joker knowledge is lacking.
In terms of insanity, they do differ. Where Joker is more of a genius/criminal mastermind who finds people's despair humorous, Jeff is someone who's overly fond of the power and thrill of killing, which is typical of a horror story and not of a comic (other than Zsasz which has already been pointed out.) In measuring which is darker...I'm not sure it can be done. It comes down to the extent they will go for what they desire, which I think for both is limitless. Jeff would kill anyone, not caring who it saddens, and Joker would humiliate or depress his target, not caring if he kills others in the process. If I was forced to decide, I would probably say Joker was darker, but that would only be due to his extreme intelligence and presence of mind, knowing exactly what he's doing and aware of what/who/how it will affect, whereas Jeff morphed into somewhat of a mindless killing machine.
In terms of appearance, I would argue that Jeff is not EXACTLY the same, but is very heavily inspired by Joker. In terms of character, Jeff is different than Joker, but heavily inspired by a majority of horror characters, unless the writer had a thing for Batman, in which case Jeff may have been inspired by Zsasz.