Kobo support stated that:
The Reading Stats and Highlights/Notes are Locally stored on the Device and unfortunately, would not be transferred to the New Device. However, the Books & Bookmarks that you have in your device would be able to Sync Across multiple devices.
I guess that means there is no read status sync.
But is it possible somehow to export highlights and noted from Kobo (whatever device/app) to something, like Evernote, a textfile or whatever?
If not, then the Kindle has a clear advantage. (On Kindle it syncs on all books, but you are only able to access highlight and notes on Amazon content, and the "personal content" does not sync to the Mac or Web version of kindle reader.)