IE has numerous security issues. IE supports broken MS variants of CSS standards. Mozilla's rendering engine tends to work faster, IMX. With the variety of plugins available, you can make Mozilla into the browser you want it to be. I suggest All-in-One Gestures and Tabbrowser Preferences. Mozilla is cross-platform (Linux/Mac/Windows) whereas IE is pretty much Windows-only (a Mac IE port exists, but development stopped long ago). IE is subject to more browser hijacks and attacks, but that's simply because IE is more popular.
Mozilla does a better job helping web development with the DOM Inspector and JavaScript console, whereas IE has nothing to help with the DOM and the JavaScript errors are wholly unhelpful. Mozilla supports tabbed browsing and popup blocking out-of-the-box. IE requires you to get an overlay (Slim Browser, MyIE2, Avast) or a plugin (Google Toolbar) -- but, of course, Mozilla has all those extensions.
Primary advantage of IE is that Internet web developer design sites just for it since it represents 90% of the browsers out there. Because MSIE uses some proprietary (broken) standard variants, Mozilla has some trouble with some sites. IMX, especially with certain types of CSS-based DHTML.