The previous version of Internet Explorer (IE) was notorious for security problems, particularly tied up with ActiveX controls. Firefox is significantly more secure than that. Microsoft has just come out with a new version of IE (the previous version hadn't had any significant updates in years) and it appears to be much better, in terms of security. However, I'm sticking with Firefox nonetheless, as I believe that open source security is typically better than closed source due to more people examining and testing the code.
This was first published in November 2006