Got a very simple proof of who is going to be wrong. This proof doesn't say if one is right but will merely exclude 1 model of the earth. This proof uses something widely reconised and easily seen by the naked eye. This test is repeatable and can be done by anyone.
Have a look at the southern cross. Its orientation is on the Australian flag. What is important is the orientation of the stars. Using the stars themselves and pair nearby (toliman) you can calculate south.
You could take a picture with your own camera if you liked for future reference.
Now imagine your in South Africa. This should put you on the other side of the southern hemisphere. The southern cross in this country will determine who is right when you face south:
FE: The calculation of south must be reversed
RE: The calculation of south will remain unchanged.
There is only 1 possibility. Only 1 can exist. It doesn't prove anything being correct, but it does make 1 model impossible.
More info on the Southern Cross:
http://en.wikipedia.org/wiki/Southern_crossEdit: Trying to less confuse people and a slight correction of facts. I had the right heart, slightly off idea on how it worked :S