There is a tricky bit to this question. Namely the fact that you can play the same account on PS3/PS4/PC. That being said, what would happen if, on the off-chance that you were playing an Au Ra Dark Knight and logged off in Ishgard on PC, then decided to play on PS4? Would you instantly lose access to that character on PS3/PS4?

That seems silly to me. If the servers were separated and you required an account for each platform, I could see how they could separate it. But as it is now, somehow I doubt it.