Firefox vs Internet Explorer
Firefox was able to challenge Microsoft internet supremacy of the browsers market as soon as it was released by the Mozilla foundation in 2002. It has proved its efficiency on different OS including Windows, Linux, BSD and UNIX.
What are the advantages of Mozilla Firefox?
Security is handled by Firefox like no other browser. It blocks Spyware and malware installation whereas internet explorer Microsoft components love Spyware, viruses and pop-ups. Well you just need to Google for the term, "internet explorer crash" to get a thorough idea, every now and then the Microsoft guys come with an urgent security update for internet explorer users. Even though Microsoft could have been the target of tremendous amount of hackers when being compared to Firefox, but still Microsoft holds the responsibility for the security holes in internet explorer. The way at which security is handled at Firefox is completely different from IE, as it doesn't rely on digital signatures, security zones and doesn't above all include the terrible ActiveX component which has always been used by certain websites to execute dangerous scripts and install malicious components on your computer. Both Browsers have a phishing protection mechanism defending against identity theft.
Tabbed browsing which allows you to open multiple documents in the same window is supported in Mozilla Firefox. This feature has only been newly applied to IE7.
Internet explorer 7 still lacks a download manager; a critical functionality which allows the user to pause/resume downloads, whereas Firefox has a built in download manager.
Spell checking which is very useful for blogging and forms fillings online is supported on Firefox but not on internet explorer. CSS 2 which is a W3C recommendation has a partial support in internet explorer and full support in Firefox, allowing the websites styled using CSS 2 to be displayed in the right way.
Above all, Firefox is an open-source project, which means that there are programmers going through the code trying to add new features, extensions, plug-ins and bugs fixes as necessary. Microsoft is a company that is hated by millions all over the world meaning it will be probably under the constant threat of malicious attacks by hackers to beat it.
If you'd like to get detailed info about the features and compatibility of each browser with the web standards you can get more info from Wikipedia. The link provides a detailed look at almost every browser on earth including Maxthon, Flock, Avant, Safari, Opera, Netsacpe and many others.