They mean the same thing generally. "I have no idea." is a bit more situational than "I don't know." "I don't know." is a very general term that means just what it says. "I have no idea." is a bit of a stronger way of saying it, meaning the person, possibly meaning the person saying it has little knowledge of the topic or the context involved in the question.

我不知道 = I don't know. 我一点儿也不知道 = I have no idea.

the same meaning but "I have no idea" is more expresive....I think...