Real question is can Superman beat the Joker?
From Reddit:
I was going to say something about this. The thing about the Joker is that he plays mind games. Batman and his Bat-Family are really the only heroes in the DC universe who can keep up on that level. Superman just doesn't grasp the complexity.
I mean, okay, sure, Superman busts through the walls and grabs the Joker, tosses him in Arkham.
Then What?
Joker escapes in a few days, ready for Superman to come at him and laces kryptonite into his laughing gas. Supes speeds in and BAM, worlds strongest hero is out on the floor. And that's just the end game.
To start, Joker discreetly plants dozens of bombs and tanks of Joker gas all throughout Metropolis, completely encased in lead boxes so Superman can't catch them that easily with his X-ray vision. He steals a TV signal and announces that they're going to explode in thirty second intervals, and he makes sure to mention that he's left at least half of them under schools with high numbers of students. He does this midday.
Then, Joker tracks down Jimmy Olsen or Lois Lane, both known associates of Superman, and shows up at their apartments. A gunshot later, they're paralyzed from the waist down and he's taken nude photos of them covered in their own blood. He records them begging for mercy the whole time, and his laughter. He leaves them disrobed, bleeding and crying on the floor. Then he moseys on over to his headquarters.
When Supes is finally done dealing with the distraction he is contacted by the police, informing him that Lois/Jimmy is in the hospital. He's handed the two pictures that were left in the blood. Superman gets mad. He hadn't realized it, but for the last 5 minutes there has been a slowly building crescendo of whimpering and laughter playing at a frequency that only he can hear. He zips off at superspeed to grab Joker.
But Joker isn't dumb. His base is an abandoned nuclear fallout shelter. Lead-lined. Supes has to come in somewhere, and Joker has gone with the old stand-by of fun house mirrors all over the place. The laughter and crying is being played at 200 decibels all throughout the shelter. Superman is confused. He's not used to this sort of psychopathy. Even Lex would never do this sort of thing.
Then the mirrors start to project the pictures. At first, they appear one-by-one, but eventually they're on all the mirrors at once. Superman is confused and enraged, his super-senses being overwhelmed. He finally finds the door leading to Joker's room and breaks it down.
Inside, Joker is dancing and laughing, waiting for Superman. He smiles when he opens the door. "I see you received my message, Superdork." He Laughs hysterically at his own joke.
Superman speeds across the floor and lifts Joker up by his throat, his eyes ready to laser him. Joker tells him that he's a hero, he's not supposed to kill. Superman calms down, and releases his hold. Joker hits his flower, and BAM kryptonite Joker gas in the face!!!
Now Superman is captured, and Batman has to come save his dumb ass.
This is all assuming Joker
doesn't ask Lex for help.
Nothing against Supes, but he just doesn't have the mind to deal with Joker.
tl;dr: Only Batman has the mind to take on The Joker, and Superman would definitely need to team up with him if Lex Luthor were involved.
Now I think that Superman's character would change drastically and he would probably do something he would greatly regret in killing The Joker if he had done that to Jimmy Olsen or Lois Lane, but that's all speculation. Here's the thing, someone with Superman's
powers could easily take the Joker, but the question is whether someone with Superman's
humanity would be able to do so. You'd have to take away Superman's humanity for him to be able to take on the Joker.