I would say OOC for reasons [@Kuro] mentioned, but I have had good luck having more sensitive stuff getting discussed via PM such as secret backstories and the like. I had a murder mystery RP that had public character sheets and a list of secret questions. Everyone had a lot of fun with the idea that not everyone knew everything about their character. But it is sort of a pain to manage if you don't wanna copy/paste the secret into a general folder. 

As always, my answer is "It depends" but having characters in the OOC is good for a lot of reasons.