I think they are mostly incompatible: the server needs to choose how to respond to a request for a private resource. Either it requests a certificate, or it responds with unauthorized. Maybe we could have a request header to choose between these options? My understanding of the matter is still scarce, but of course being able to use curl on the command line with its built-in support for client certificates would be great.
As for webid-oidc, there is a huge difference in that the client needs to remember the name of the solid pod. If I understand correctly, the browser will not fill it in, because it could leak information in the DOM.