What difference does it make?
Because of certain people who take the bible literally.
It makes a BIG difference.
If Genesis is not the authoritative Word of God, then the tests determining who is and who is not a real prophet of God contained in Genesis are suspect. And if the test of a prophet is suspect then the selection of prophets in the Jewish canon is also suspect. And if the prophets are suspect, then the prophecies of a messiah are suspect. And if the prophecies are suspect then the messiah Himself is suspect. He is doubly suspect because He quoted the works of Moses as authoritative and referred to creation.
For example when Mohammed proclaimed himself to be a prophet the Jews and Christians laughed at him because he clearly failed the test of a prophet that Moses laid down.
In short, if Genesis cannot be relied on, then we are free to pick and choose from all scripture as we wish or disregard it entirely. Everything we know about God and right verses wrong is subject to our scrutiny and our whim.
There are not two incompatible creation stories. One is more detailed and an elaboration of the other.