Well i have both installed on my Home PC, and i use both for different tasks. Ultimately though IE is king within a Corporate environment. And this is because:
The most significant advantage of IE is that you can centrally manage it using Group Policies. You always want to configure all applications as homogenous as possible in a big network. Sometimes it is necessary to change the settings of all web browsers in your company. For example you might want to change the start page of all browsers or enable/disable certain functions or add new bookmarks, etc.
When it comes to security in a corporate network, the main question should be how fast and how easy you can patch all your computers. The larger your network is, the more important this point gets. Firefox has an integrated update mechanism which is quite useful for private users, but doesn’t help much in a corporate environment. Because of security issues, normal users are usually not allowed to install software on their computers which also means that they can’t install patches.
If you are a Windows administrator, you probably know that Microsoft offers a free patch management solution. WSUS (Windows Software Update Services) certainly is a great tool. Of course, you can patch IE using WSUS. There are third party patch management solutions which also support Firefox though. If you are already using such a program, patch management might not be something that troubles you too much when you have to decide which web browser to use in your network. However, if you are also using WSUS, patching IE might be less time consuming than patching Firefox with a third party solution. At least, this is true for patch management solutions I’ve seen.
There are many desktop applications which use the rendering engine of IE to display HTML files. There also server-based applications which need an IE and won’t work with just another browser. With the success of Firefox at least the latter’s argument doesn’t hold much anymore since many webmasters don’t want to lock out this large clientele.
However, there are still many desktop apps which are IE dependent. Some of them aren’t dependent on the rendering engine of IE, but integrate themselves in the user interface of IE. Adobe Arcobat is such an application for example. Even if you don’t have one of them in your company now, you’ll never know if this might not change in the future. The point is that if you need IE anyway, why you should deploy and support another browser in your network?
I wouldn’t recommend it for corporate use in larger networks. There are exceptions of course: If all your desktops use Linux or Mac OS. But if you have Windows desktops, the only reason I could think of, is that you really need a certain feature of Firefox which you is not available in IE.