They share a lot of similarities, but have one big point of contention. That’s the entire point. He’s a former Robin, does all those things associated with Batman, but breaks the no killing rule. That’s his entire shtick. That’s not fundamentally different. That’s a twist on something already popular that fans are familiar with. Under the Red Hood needs Batman as much as it needs Jason Todd. Even more so. Because the entire point of the story and it’s appeal is how it relates to Batman. The one Batman game didn’t even call him Red Hood but Arkham Knight, and kept his identity secret for the majority of it. As it’s the story they wanted not the Red Hood brand. To claim the Batman games were centered around Red Hood as much as Batman is just widely inaccurate.
Harley Quinn branched out into other brands like SS. Her appeal and adaptability isn’t dependent on a particular Batman story. We haven’t seen any of that kind of agency with Red Hood. We have with Nightwing though. Red Hood hasn’t ever been pushed as an independent brand and DC has displayed no interest in doing so. His growth in the mainstream hasn’t extended beyond one Batman story.
With Nightwing, he was playable in those games before Arkham Knight even came along. What’s more he at least appeared as Nightwing. Those games even had a lasting impact on the character with how they presented his weapons. Nightwing appeared in everything Red Hood has, in addition to multiple more tv shows and cartoons. Can they do better, sure, but it seems your trying to martyrdom him in comparison to Red Hood. When his mainstream profile is actually probably larger and has displayed more independent potential as he’s less beholden to one particular Batman story.