I think the complexity of (most of) Prince's work makes it almost impossible to define or analyze with traditional terms. The songs are created and recorded "in one piece", and it's hard to distinguish separate elements such as the actual composition, the arrangement, the performance, the production, etc.

It's interesting that, considering his huge catalogue, Prince has had relatively few of his songs covered by other artists. But I think that's because the greatness of his "compositions" is not all about melodies and chord changes, but also about all the other elements involved in the process.