There are a few sites that FF can't handle (National lottery -UK for example), but there are less and less all the time.
I use FF for 99% of the time now but the family still use IE mostly. FF is default though so they probably don't even notice most of the time which they're on.

There's no reason not to use both. If I ever have a problem with a site there's an extension called IEView. Just right click on the link and it opens the page in IE.

Tabbed browsing rules ok Why IE doesn't have it now is just plain lazy on MS part!