We know that they were both said at the same time, but what was actually written on the לוחות themselves. It is clear from the gemara that only 1 of them was written as the gemara comments that the ם and the ס were בנס, if both זכור and שמור were somehow written בנס the gemara certainly would have mentioned it.
R' Yaakov Kamenetsky addresses this question (in ואתחנן) and claims that זכור was written but the קרי was שמור. He says this would apply to all the other differences as well (קרי וכתיב).
However, this is very difficult as the end of the דברה of Shabbos is completely different, in יתרו it talks about the 7 days of creation and in ואתחנן it talks about יציאת מצרים. On one word I can see saying קרי וכתיב but not on a whole pasuk.
Has anyone seen any other mefarshim address this issue?