"Is she a director or an actress?"

I think there's an important difference:

• чи is used to suggest two alternatives to choose from (Вона режисерка чи актриса = I want to know what is her occupation: is she a director? Or is she an actress? The difference between actress and a director is important)
• або is used to suggest two options both of which are acceptable (Вона режисерка або акторка = I want to know if she is either a director or an actor, I don't care who exactly, I just want to know if she works on movies or not).