Might as well throw Julien Donkeyboy in the mix too, speaking of Kids and Gummo.
I'm big fan of all these directors being mentioned on this thread...so, yes, I'm somewhat demented... :)
In comparing them, Aranofsky's and Korine's films are disturbing in a much different way than Lynch's. The former are sensational, aiming to smack you in the face with "reality." Plot lines are understandable and the characters (outwardly anyway) are relatable. This is definitely true for Requiem and most all Korine's, but not so much Pi, which is more intellectual...both in terms of plot and production. (And actually similar to Lynch's Eraserhead in many ways.)
Lynch's films, on the other hand, are more art for art's sake. Lynch doesn't really care if you completely understand his films, nor does he want you to. He introduces characters and scenarios that are very bizarre and unrelatable. This is what makes his films disturbing...the fact that we can't relate, whereas films like Requiem and Kids are too human, too relatable for us. (enough italics for you?) For instance, I don't assume KatieB main-veins, but she can relate to Wayan's when he was shooting up...and this freaked her shit.