Most Oxygen Theme websites seem to have a great navigation menu which collapses into a compact ‘MAIN MENU’ button when viewed on a mobile smartphone or if you make your browser window small. When clicking the new button the menu options cascade out below.
The other site is on WordPress.COM – even the same theme is not always identical between the .COM and .ORG versions. So that might be the difference. You might be able to look at all the CSS code for that site and see where they are different.