Mozilla is seemingly addressing security patches a lot faster than its competitor Microsoft. In 2005, it took Microsoft at least 38 days to address a publicly known and actively used exploit. Unused exploits took MS 256 days to patch. Firefox, on the other hand, only took 16 days to seal comparable vulnerabilities.
The difference lies within Firefox’ open nature. The public knows about the flaws and is allowed to look into the code, possibly even contributing to the patch. Aside from this fact, there’s also the the market-share factor. Internet Explorer still owns 85% of the browser-market, making it much more of a target to hackers, because of this fact IE experiences substantially more security issues.
Whichever browser you choose, keeping your software up to date is a must.