It is question of your "taste". Well configured security parameters and critical updates can achieve good reliability and security of your computer from I-net.
But using IE is little more "dangerous" than using any other browser, because it is most widely used web browser, so hackers and "virus makers ;o)" concentrate their "work" on this. This is comparison of security. True is, that many other browsers provide better user interface(plugins, mouse gestures,....). I don't have personal experience with Mozilla therefore I described this from this wiev.