Answer: Mozilla screws up rendering very badly on a wide cross-section of sites and images. Some forum software gets messed up so badly it's barely usable, if at all.
The security is actually a myth. Firefox has been proven as vulnerable as IE. With Javascript exploits now abounding, Firefox is powerless to stop them. Enabling the noscript plugin actually disables the biggest majority of your browsing experience. Secure, perhaps, but at what cost?
Numerous exploits have gone unpatched for months, even years at a time.
Consistently beta software. The fact that's it's open source makes it relatively easy to code exploits.
Incompatibility with numerous multimedia/interactive content plugins unless you use the IE plugin, which renders Firefox every bit as vulnerable as IE7.
Plugins have been proven on numerous occasions to have security flaws, and provide rogue programmers an easy ability to code exploits into plugins (some plugins have been found to have such exploits in them).
Memory leak issues which get worse the more tabs you have open.
Many users report frequent crashing.
No speed advantage. In fact some users report slower rendering speeds than Opera or IE7.
In short, for the most part Firefox is a piece of crap, especially from a web developers point of view, but also for the user. However, Google invests over $50 million a year into Mozilla in an effort to dethrone IE7 as the king of browsers. It has a vested interest due to the Google searches, etc, coded into Mozilla.
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Mozilla (Firefox) is useful as a lightweight alternative to the more commonly used internet Explorer.
One advantage is the easy to use plug-ins that ask if the user wants to use them when they've been installed. This makes malware harder to get on your browser (and machine).
One disadvantage of Mozilla products is their slightly less adopted formats. I have encountered a few payment sites that don't work properly with Firefox, but the number is dwindling as Firefox is becoming more mainstream.
Internet Explorer was developed by Microsoft and has been the most widely used browser for years. It has had some stability problems and has been encroached upon by Firefox over the past few years. Many find Firefox to be updated more often which fixes security issues that have plagued Explorer. It may well be that personal preference is the real difference in the two.