IE and FF are the only 2 browsers which use Web standards. So most nearly if not all the internet will work on both. It's very unlikely a page will not work on at least one of them.
But firefox is quite alot better at coping with poorly coded or broken HTML, whereas IE isn't as good. This was nice for me, and when I ran a website, and for a while a forum, I coded alot of stuff myself... and often had IE users reporting to me "Your site doesn't work!".
Best bug was on a forum, I once forgot to close a piece of code... and left the reply box without a size limit, so on IE it expanded into infinity until it crashed. Firefox fixed my code itself.
I laughed so hard, I nearly wet myself when I tried it for myself in IE.
To be honest though, the IE vs FF vs Opera vs Chrome argument is much like Ford vs Chevy or Windows vs Mac vs Linux. All have pluses and minuses. I prefer FF. It's fast, simple, and does what I want. IE has simply copied it, like FF copied things before it. FF however made it popular through using viral advertising on the internet, very, very, well indeed. Free advertising is the best, when customers do it for you.