What I mean by generic is that it feels like you could take the tragedies/events that made them go bad, apply them to any other character, and you'd get basically the exact same result. There's nothing about them that feel specifically built around being stories for Superman or Jason Todd, at least not in comparison to stories that did the same idea way better.

For example, sick as I am of the "Superman gone bad" trope, the Justice Lord version from the DCAU's "A Better World" two-parter is the one that I think has done the concept the best. Not perfectly, but still pretty good and it's in no small part because of specifically what made that version of Superman go from classic hero to totalitarian ruler.

The Justice Lords' timeline played out basically like the main DCAU did except eventually Lex Luthor managed to work his way into becoming president of the United States, where he eventually had The Flash executed and put the entire world on the brink of a war that was threatening to tear the whole thing apart, which ultimately leads to a confrontation between him and Superman in the White House where in his desperate state he basically goads Superman that all of this is his fault too.

From the beginning Superman's known Lex was a bad guy doing tons of illegal and immoral crimes. But he constantly used his money and resources to keep the law away and keep whatever proof Superman could bring up for his crimes not stick. He was an enemy Superman couldn't just solve with his fists...except...he totally could solve him with his fists. He deliberately held himself back all those years because he believed using his powers to kill or maim Luthor with be unethical and a violation of his basic human rights, with Luthor's taunts also claiming that he didn't do it just because he liked being the hero.

And in the Justice Lords' timeline, where did holding back lead? The Flash is killed, the world is on the brink of a war that'll tear it apart, and Lex Luthor is in a position of power he never should have been allowed to have.

Yes, he has other ways he could potentially stop Luthor without killing him...but would he just do the same thing all over again? When is enough finally enough?

And thus, he finally, of sound mind and body, kills Luthor. Afterwards he and the rest of Justice Lords start imposing their will on the world to keep anything similar to what Luthor had done from happening again.

The Justice Lord version played into Superman's history, especially his history with his greatest enemy, and the struggles he's consistently had to deal with. Regardless of whether you agree with his decisions, the conflict that caused him to turn feels like something that was constructed around Superman's actual character first and foremost rather than just being something that was slapped on him to make the story happen.

By contrast there's what caused him to turn in Injustice, which was the Joker tricking him into accidentally killing Lois and their unborn child, which also sets off a nuke that destroys half of Metropolis, after which he murders Joker in his raging and grieving state. Some time later he and various other heroes create The Regime to oppose their will upon the Earth to keep similar tragedies from ever happening again.

This...doesn't work nearly as well as the Justice Lords, for a few reasons, but the biggest being that Joker is not a villain Superman has a history with. They have encountered each other and fought on occasion before, but very infrequently. Joker is not one of Superman's villains and so Injustice Superman's argument that he could have prevented such a tragedy if he was more forceful and willing to kill rings somewhat hollow because it doesn't really apply. It worked for the Justice Lord because he and Lex have a very long history where Superman many, many times had to ask himself the question of whether he should just kill him, but Joker? Replace him with any other villain outside of his rogues gallery and it's the same problem. Reverse Flash, Sinestro, Ares, King Orm, Black Adam. Injustice Superman's argument is basically "I could have prevented bad things if I hadn't held back against this villain I never interact with and never had to make the choice to hold back against before."

There's also the problem of the state of mind he was in. When Injustice Superman killed Joker, he was grieving. He was enraged. He was not thinking clearly and wanted revenge. Again, it feels generic and not tailored specifically for Superman, it feels like any other superhero put through the same experience of being tricked into killing their family and destroying a city would react exactly the same, and yes, that includes Batman. In fact it actually would work better if it was Batman, not only because Joker is actually his biggest enemy whom he has a long history with, but even replacing joker with another villain, one of Batman's big thematic struggles is justice over vengeance. Him lashing out after experiencing such a cruel tragedy and basically inflicting his pain on the rest of the world by taking over fits as a dark turn for his character way better than it does Superman, whose thematic struggle is to inspire people to be better like he knows they can be rather than using his great power to force them to behave because he believes they can't be better...like, you know, the Justice Lord version.

There's a lot more I could say about why Injustice Superman doesn't work for me, not the least of which being that the story (both the games and comics) unintentionally make it clear that the Regime universe and the regular universe are actually very different to begin with (Injustice Superman and Lex were friends rather than ever enemies, Aquaman only recently became known to the Injustice world rather than a longtime member of the Justice League like in the regular universe, etc.) and thus means regular universe Superman isn't really in as much danger of becoming like his Injustice counterpart as it'd like you to believe, or the bullsh*t ideas it has about Lois being the only thing keeping Superman tethered to his humanity and her death "being the first time in his life he's ever been vulnerable", which are horrible misunderstandings of Superman's character. But this rant is about the tragedy and events that turned Superman into what he is in Injustice, and like I was saying, it just feels generic. Unlike the Justice Lords, or Red Son, or Kingdom Come, Injustice doesn't feel like a story that asked "What would it take for Superman specifically to go bad?" but rather a story that thought about what it would take for superhero to go bad and then slapped that onto Superman. The problem isn't that the story doesn't make sense when applied to Superman, it's that there's no real aspects of Superman himself being used for that story. He's just the big stick that's used to make the plot happen.

And then there's Jason Todd in Batman: Arkham Knight. He was made into the main villain of the game, the titular Arkham Knight, likely as a loose adaptation of Under The Red Hood, where he was also serving as a villain for Batman, namely The Red Hood.

The problem? Jason as the Arkham Knight is heavily lacking in nearly everything that made him work as the Red Hood.

In the comics (and the animated movie, which more people are probably familiar with), Jason Todd was the second Robin who was eventually captured by Joker, beaten to near death with a crowbar, and then blown up along with the building he was in to finish the job. Many years later he's brought back to life (in some continuities through the Lazarus Pit and in some through Superboy Prime punching reality) and returns to Gotham as the Red Hood, an alias used by many criminals in the past, including Joker before he became Joker.

Jason, at least in his initial storyline after returning from the dead, works for a few reasons, one of the big ones because how he challenges Batman's methods and mindset as he's determined to be a better Batman than Bruce ever was. He doesn't believe that crime can be stopped but that it can be controlled, thus he takes over various gangs and their drug operations, letting them continue the harm they do under his protection but steering them away from certain activities like dealing to kids. He believes that there are criminals who need to just be put down and thus he's much more lethal. Whether you agree or disagree with what Jason's doing, his grievances are at least somewhat understandable, especially given who he was before he died. Gotham seems like it's just continued to get worse while he was gone and he was hurt and angry that even killing him wasn't enough for Batman to finally decide to kill Joker.

Jason in Arkham Knight...hates Batman because Joker tortured him.

I'm barely exaggerating. Both the game and the tie-in comics make it clear that Joker conditioned Jason through a year of torture to hate Batman and want revenge on him, thus why he does everything he does in the final game.

Again, like with Injustice Superman, it's not that this doesn't make sense as something that made Jason go bad, it's that it's generic. There's nothing about it that using any specific aspects of Jason Todd's character or history. If Joker had done the same thing to anyone else, he would have achieved the exact same result. He could have taken someone random off the street and it'd be exactly the same! While Red Hood Jason has actual personal reasons why he's angry at Batman, Arkham Knight Jason is basically the Spongebob meme of "Do this because I told you to.". They don't even try to play up Bruce replacing him with Tim, which could at least have given more weight to Jason feeling abandoned and that Bruce never cared about him. Joker mentions it once in the flashbacks and Jason never brings it up in the present, which gives the impression that wasn't really a factor in anything. He brings up Barbara more against Bruce than he ever does Tim.

TL;DR: Injustice Superman and Arkham Knight Jason Todd do not work for me because the tragedies that made them fall are generic and don't feel like they actually use any of their actual character. Apply the same tragedies that happened to them to any other character and you'd get basically the same result, while better done versions like Justice Lord Superman and Red Hood Jason Todd feel like those stories are more specific to them and can't just be slapped onto any other character to the same effect.