I believe IE looks for <siteroot>/favicon.ico and shows the icon in Favorites. It needs the link rel way to display it on the Address Bar, but only supports .ico.
Mozilla can be selected through UI Preferences to show website icons (link rels, any file format) in the Address Bar (enabled by default in Netscape), and through hidden prefs to show website icons that IE shows only in Favorites (i.e. the <siteroot>/favicon.ico file). Opera is showing the <siteroot>/favicon.ico file in the Address Bar as I go to
team188.com, so it looks like it has similar behaviour to Mozilla.