If we look at Secunia's criticality graphs (1 and 2) we can see that Firefox has 0% extremely critical and 8% highly critical bugs while Internet Explorer has 14% extremely critical and 27% highly critical bugs.
Comparison Of The Two Browsers
The biggest challenge facing Firefox is that even though it offers tabbed browsing, live bookmarks, text zooming, pop-up blocking and a superior user interface, Microsoft's Internet Explorer is still the most widespread browser. After all, every copy of Microsoft Windows sold includes a version of Internet Explorer and every Web site is optimized for Internet Explorer.
A Google fight reveals us: Internet Explorer - 36,000,000 results, and surprisingly, Firefox - 31,000,000 results. Still, Firefox has its flaws like crashing while trying to view PDF files and taking a lot of time to load. If the next IE version would support tabbing and would be 50% more secure than before, Microsoft would surely maintain dominance in the field. According to W3Schools, Firefox has slowed in growth over the past few months and it now has 21% of usage share, compared to IE6 which has 64%.)
Expectations for the future
At the present time Firefox seems more secure than Internet Explorer, but what will the future bring?
An interesting alternative is SecureIE which costs 30$ and seems to outperform Firefox and IE in the security field.
Microsoft has made spyware prevention one of its primary missions as well, so its browser may improve too in that regard, but for now, switching browsers is the best defense against malware.
As more and more users dump IE due to its lack of features and move towards a faster and more efficient alternative like Firefox, virii and spyware programmers will start using it as their new "feeding ground."