In terms of goals he's similar to both.
No he isn't. Vergil is just a power hungry douchebag.
Jason Todd after getting killed came back to become the 2nd Red Hood who really isn't a villain so to speak. He's an anti-hero. He fights crime but uses lethal methods which usually puts him against the Bat family. He fights to save lives to an extent.
Damien Wayne however actually does respect his father and tries to live up to his expectations. Of course being raised by Talia's crazy family he was taught to kill at a young age and can be very brash and violent.
Vergil is petty, selfish, and straightforward. He's so one dimensional and Vergil's ideals don't really line up with Jason Todd and Damien Wayne who would also stand up to fight against a person like Vergil anyway.