From a user perspective:
Mozilla advantages:
* Tabbed browsing. You can't know how awesome it is until you use it. IE doesn't yet have it.
* Built in popup blocking. IE depends on third party popup blockers, and most of them suck. Some will disallow popups even if you click on a link.
* Per site permissions.
* Ability to disallow certain javascript annoyances. Specifically it can disallow javascript the ability to hide menu/status bars, resize windows, move windows, etc. If you've ever been hit by spyware, you can see how that's a good feature.
* Less susceptible to malware. Because mozilla has its own set of bugs and exploits and because it implements technologies differently, spammers, hackers and spyware folks have to write special code to hit mozilla users. Because so few people use Mozilla, they usually don't bother.
Disadvantages:
* Many websites that run major web services disallow Mozilla.
* Few websites seem to bother to test on Mozilla and on many websites pages don't display properly. This problem is slowly going away.
Those two disadvantages are a big enough problem that many folks have to keep a version of Netscape or IE handy to be able to use those websites. The second problem is HUGE when it comes to javascript driven web pages.
* You have to reconfigure all your embedded objects. That usually includes Flash, Java, etc, etc.
* You have to download and install Mozilla. It also updates frequently and you'll want to keep it updated. Why go through that hassle if IE (already installed and configured) is good enough for you? This is an even bigger issue when you consider the first 2 disadvantages. Why download a configure new browser (and constantly update it) if it won't even fully replace the browser you already have and use?