I've never watched "The Blacklist", but now I got curious and checked out it's synopsis. Right, "The Mentalist" sounds like it. However, what matters is how the showrunners implement the idea of having a criminal work for the FBI. I could imagine that both shows are still very different, even though the general idea is the same.
Regarding Psych I don't see much similarity. Then again I only saw one or two episodes of Psych. But didn't the main character claim to be a real psychic? With "The Mentalist" it's the other way round. Jane usually doesn't want people to believe he is a psychic.
Surprisingly I enjoyed the reboot. It brought some fresh air. "The Mentalist" benefits from it if characters are not restricted to California any more. Furthermore, I like the new characters.