How RHATO and RHA deal with the issue of killing.
Some have written Jason off for taking lives. Some feel that there isn't enough death being dealt in these books. This is mainly an examination of how Jason deals with the subject. In scenarios when terrorists are attacking he doesn't hesitate to end the threat permanently. When working with Gotham and some other heroes he doesn't aim to kill. That said he doesn't kill everyone that crosses him and does show some restraint outside Gotham.
The All Caste taught him that death was a gift and viewed it as an intimate thing. Jason was still dealing with being resurrected and didn't follow all their teachings once he left. After Kori saves him Jason realizes how he's failed to keep up with what he was taught. When dealing with Suzie Su, a person he knows the world is better off without, Jason admits to himself that he'd take no joy in killing her. This plays a part in her turning up later on as he didn't make sure she died. When they meet again Jason actually offers her a chance to live if she walks away from vengeance. Suzie refuses to and he ends her threat immediately after because he's not going to give her another chance after she squandered the last. Jason kills to prevent villains from destroying more lives and Suzie had no problem taking a hospital hostage just for revenge.
Not long after fighting Suzie the Court of Owls unleashed their undead assassins the Talons on the bat family. Jason actually has one of the least violent encounters with his own Talon Xiao Loong. Once he discovers the link they share--returning from the dead--Jason becomes more empathic and actually tries to talk Xiao out of his deathwish. Ultimately he agrees to grant a mercy kill. Much later when he encounters a telepathic alien that also wanted Jason to kill him the guy admits he chose Jason because he was the most merciful Outlaw. Kori of course would have dragged out a death since the alien tortured her as a child. Roy isn't mentioned but maybe he would have let his feelings for Kori prevent him from ending her tormentors' misery.
All things considered Jason usually grants a quick death. He doesn't play around with his enemies with the Joker being the rare case where he doesn't just shoot him and be done with it. To me this suggests that even though he feels compelled to take extreme force to save the lives of innocents Jason isn't cruel. Joker made his death agonizing which may be one of the reasons he gets it over with quickly. There's also nothing to be gained from prolonging it and he doesn't have any sadist glee in doing more.
Back in RHATO #5 Jason refused to kill the towns' people because they were innocent people that didn't know any better. In the alternate future of Futures End Jason does give the cops a chance to walk away but it shows how much he's changed that he's willing to kill them just to get to one man.
It's easy to label Jason ruthless but that doesn't mean he likes what he does, he just sees it as a necessary evil. He has shown mercy by killing those that want to escape a painful existence and it's hard to imagine Batman or others dealing with such a thing in a satisfactory manner. There's also the case of Simon Amal/Crux. Kori wanted to kill Simon after he attacked her, Roy thought it would be overkill and it fell to Jason to decide. Now I didn't care for the explaination Lobdell gave for Jasons' choice because as an Outlaw Jason doesn't follow laws and Simon did try to kill his friend. I believe Jason had other reasons he didn't want to own up to like feeling empathy for Simons' story and/or the fact Jason wasn't even there for the fight. He chooses to let Simon live by tossing him in Arkham and this choice was a good call since it helped rehabilitate Crux.
It would be a neat twist if Jason gets an ongoing arch-nemesis who's immortal or Jason can't kill because of reasons (ex: the bad guys' death would start off a full scale war .) There's a lot to work with that other superhero stories can't get into.