I don't know of any way to sync the libraries of the two.
In theory you could use a PC connected to both eDGe's via separate mini-usb cables to file-sync the Library folders but this wouldn't include the Library database(s), or a similar method. Someone like mrspaceman, who's done some work investigating Library access, might have some insight.
So far, my usage of the two is quite different, so that the books I read on the EE are different from those on the PE (i.e., technical vs novels), although only the novels are important in terms of where I left off reading. Similarly, my Journal usage on each is different (meeting notes vs grocery lists and reminders), the former often being transfered to my main PC anyway. The PE Journal page size is much smaller, so it would probably show up as taking a smaller portion of the larger EE eink screen. I've not been able to find the .esj journal files lately, so I can't even try transferring them (although it wouldn't work anyway since the Library doesn't pick up new files dropped in its storage folders). Exporting to PDF is different animal, of course, and I know from viewing PE Journal PDFs on my PC that they show up as "tiny" pages (i.e., the size they are on the PE).
Syncing other things like browser bookmarks and app settings is hit and miss. Some apps have settings import/export, and there are apps that will import/export browser bookmarks. Ultimately it's a bit of work to get the new eDGe set up with the same setup as the existing eDGe. Dropbox certainly makes things easier.