Unlike Tim Sale's basically iconic, game-changing Joker, Paul Pope's Joker only appears in one place ("Teenage Sidekick" from his issue from DC's SOLO series) but it is, in its own way, as weird and interesting as Sale's too big for the body, mile-high demonic smile Joker from Long Halloween.
Paul Pope's Joker is Cesar Romero from the Adam West "Batman" series just, rendered with the tons of lines, too-big lips, and the overall slightly manic style in which Paul Pope renders everything. If we weren't viewing Romero from the distance of cameras and then our own televisions, and were instead, inches from his laughing face, he'd probably look more like this Pope drawing than we might expect. And that's the initial brilliance of Pope's Joker; he saw beyond the decades of irony and hipster guffaws that've rendered the Adam West series basically irrelevant and realized that in most ways, the sickest and scariest incarnation of the Joker remains Cesar Romero's.
It's the Joker in the real world...his make-up's toilet bowl white and slathered on, hinting at the real human being underneath. That it's so much more obvious that an actual human being's under the make-up in Romero/Pope's makes the Joker's devotion to his anarchic persona even more absurd. He's in denial of his humanity and he's pathetically in denial that we know he's a human being and not some crazy, evil force (as he's stupidly portrayed in The Dark Knight movie).
And the hair! His hair's not perfectly dyed green but like old-lady-dyed-her-hair-blonde-and-then-went-swimming-and-the-chlorine-turned-it-green, green. Supervillians, especially in the heavy psychological realms in which even the goofiest Batman stories operate, are crazy, messed-up sick people, and seeing an older guy looking like Cesar Romero as the Joker would be horrifying. Seeing Sale's joker would be scary, but scary because he's deformed and not-human looking and unlike anything you've ever seen before. Rather than create a new image of Joker--something the brilliant mind of Paul Pope could've easily done--Pope chose to go back and revitalize a Joker and put him back into context as a really scary dude.
In another way, it's also the Joker that most closely resembles Pope's prior work and in that way, maybe Cesar Romero's Joker spoke to him or maybe, given Pope's comic-nerditry, really was a huge influence on how he drew. The big lips especially, invoke nearly all of Pope's creations as well as Pope himself. Most portrayals of Joker--again, except Sale's super-deformed Joker--suggest that the Joker applies clown make-up to enhance his look and extend his lips, but Joker's giant lips here just have lipstick applied to them, they're already gigantic. In Pope's world, everybody kinda looks like this. Some readers and critics have hinted or outright stated that the similarities between nearly all of Pope's creations and Pope himself (see above self-portrait) is some odd form of egomania or self-obsession, but it seems more in the vein of the pervasive Grant Morrison doubles in so many of Morrison's comics. More of some weird, meta attempt at self-reflection and self commentary than something as simple as turning the world into your double due to inflated ego.