We use (1) to mean that there is no difference: "Lying is no better than stealing." (2) is used to correct what you consider inaccurate: A: "Coffee is better than tea." B: "Coffee is not better than tea - tea is healthier."

no better suggests equality. You are no better then me. We are the same. is not better suggests inequality. I am not better than you. You are better than me.

I dont think there is any difference. 2nd sentence is formal, 1st one is conversational.

yes there is a slight difference A is no better than B - implies that they are of the same quality, however A is not better than B - implies that B is better.