The moon in the southern hemisphere is not quite the same as the moon in the northern hemisphere.
I noticed two main differences. First, there is no man in the moon in the southern hemisphere, and second, in the south the moon appears to moves from right to left across the sky, east to west via the north (rather than east to west via the south).
It would appear that in the south one sees the other side of the moon - the back of the man in the moon's head, or under his chin, rather than his face.
After a lot of pondering and a little bit of internet research that just drew me into the complexity of the whole issue (the tilt of the earth's rotation axis / elliptical orbit path / the sun's gravity / and more..) I am still not exactly sure of the orbit path of the moon around the earth and its relationship to the southern and northern hemispheres, but I did discover that the moon waxes and wanes and opposite directions - in the north the new crescent moon is seen on its right edge, in the south the new moon starts on the left.
This is not the place for a technical discussion of the moon's orbital behaviour, more a place to note these relatively small but interesting and particular changes in the stuff that surrounds us. If you look at the same thing from another angle you see something else.