You are not comparing positive and negative of the same thing; there is a difference between 'he has a banana' and 'he does have a banana'. These two phrases can mean the same thing, but not necessarily, depending on context and emphasis.
The negatives of these are also different: 'he hasn't got a banana', 'he doesn't have a banana'. Again, although 'doesn't have' is usually a better way to say that the person has no banana, there can be subtle differences in the meanings.