Those two statements can be used to mean the same thing. However, the second one is more specific. It defines "business" as the area of no cooperation. The first one includes everything.

Most people would say: "I want nothing to do with you."[ I don't like you and I don't want to associate with you. "I have no business with you." is a more polite way of saying the same thing.

I would say they are the same, just the second one more polite. I have nothing to do with you sounds very rude, to use only with someone you really dislike or someone you really want to cut any kind of association at all.