if all you want to do is make a single snapshot or sorts of one site and have that display on the other, then using the built in backup/restore might work. This method may wreak havoc on any hard-coded links in your code since the domains on both servers probably won't be the same.
If you want both sites to mirror each other constantly it will take a bit more work. I've never tried anything like this but from what I've read in the past, something like rsync may be the ticket.