I had a look at the white wires that are connected to the positive battery terminal via red block connectors. They both seem to be fine.
When you say they should read the same, is that the alternator + and ground should be reading the same as the battery + and - when running? If so, my alternator is working, but not charging the battery. I checked the 65 amp battery fuse and it appeared to be okay.
My problem seems very similar to this http://www.micra.org.uk/threads/electronics-issue.55187/