The Bat-Family and Super-Family have long been the closest in DC comics, with Nightwing taking a huge amount of inspiration from Superman, but true to form, Red Hood followed his own path when it came to making a Kryptonian ally. Almost every iteration of Robin has their own Super-connection: Dick Grayson has the Man of Steel himself, Tim Drake has his best friend Conner, and Damian Wayne has Jonathan, DC's new Superman. As for Jason Todd, he struck up an interesting friendship with a Superman clone who has things a little backwards. He proves that while his friendships are less orthodox than Nightwing's, that doesn't make them any less admirable.
Nightwing has always been a huge fan of Superman, and the pair have had some iconic team-ups. In fact, after ditching Batman, Dick Grayson chose his new name based on a Kryptonian legend Superman told him about the original Nightwing. While Nightwing's relationship with Batman was on the rocks, Clark was someone Dick felt he could trust and turn to for advice while maintaining his independence. While Dick has since returned to the fold, his bond with Superman remains incredibly strong.
In Red Hood and the Outlaws #3, by Scott Lobdell, Dexter Soy, Veronica Gandini, and Taylor Esposito, Jason befriends Bizarro, the black sheep of the Superman family. When they meet, Jason sees himself in Bizarro, who he affectionately calls "Big Guy." He sees someone brought to life against their will, reflecting his own resurrection. Not only that, but Bizarro is viewed as a failed experiment, just as some comment on Jason being a failed Robin. Jason even goes out of his way to purchase a Superman doll to make Bizarro feel more comfortable when he speaks to him. He remarks that the "closest [he] came to a toy was a hot iron" and while he struggles with "family stuff," he makes an effort for someone everyone else views as a monster. As the series' name suggests, these two are just a couple of outlaws. They're trying their best, even if no one else understands. Neither the Bat- nor Super-families particularly wish to lay claim to Red Hood and Bizarro, but they've got each other and make each other better, even as their relationship flips the mentor/mentee bond of Nightwing and Superman.
Jason admits that Bizarro is, strangely enough, the first guy friend he's made since he was brought back to life. While Jason would never admit himself to be the "leader" type like Dick, Red Hood becomes a mentor figure to Bizarro. It's the type of bond Jason is sure Batman would disapprove of, but then most of his actions are ones Bruce doesn't support. However, Jason's done with trying to live up to the expectations of others. He flips every aspect of Nightwing's move to solo hero, becoming an anti-hero who doesn't play by anybody's rules but his own. He'd rather adopt an unstable Superman clone than depend on the original as his new moral compass.
It's Jason Todd's outsider identity that makes him unique in the Bat-family. Growing up on the streets, he's a little rough around the edges, but his sense of justice is unwavering. Even while befriending a potentially-dangerous Superman clone, Red Hood's compassion for the outcast shines through - he's not Nightwing, but he's learned to be a great hero without sacrificing his identity.