I installed Office Professional 2013 on a computer that had been running Office 2010. When I open a .docx document, it opens in Word 2010.
If I try "Open with" and "Choose default," Word 2013 and Office 2013 do now show up as choices in "Other Programs." I browse to WinWord.exe in Office 15 and choose it, but it makes no difference. The default is still Word 2010.
Can't image why you would make it so hard to use the new version.