This is my opinion.
I see one difference: this white paper focuses on permissions granted by people to applications, while Solid is more about permissions granted by people to people. This means that it is possible to view Solid as a social network for any purpose, whereas there is no such thing with the MyData white paper.
Here is an important point in the white paper: if you transfer the data to somewhere else, how do you tell the applications where it is now? In Solid, the data is represented as HTTP URIs, so you can move the data without changing anything, as long as you keep the same domain name.
I’m very satisfied that the MyData white paper uses the notion of interoperability. This is really what we need most. It is very hard to achieve though, so I hope they will consider our way to do it, or find another way that is both close to how the web works right now, and that allows users to recover from their mistakes.