3 years ago I would've been tempted to say IE was much better in the business place since it did have the backing of Microsoft behind it. While in some people's eyes that's a bad thing, it does mean that support is much more readily available - posting on Mozilla's forums can take up to an hour or so for a reply.
As for the safety/security aspect: ActiveX is inheritantly insecure. So much so, that it's the only security aspect that should be a problem if the IT department know what they're doing: Users of business (and educational) computers should not be allowed to install or modify essential files anyway, so the only way viruses could be installed (aside from the local-user's profile) is via system-level-exploits, which ActiveX was pretty famous for - although it's not so bad these days.
IF the system is secure enough in this sense... there really is hardly any difference between firefox and IE. Although I reckon some long time users will be slightly miffed at not having the menu-bar in IE7/8 - I know a lot of people that were totally confused when Office 2007 came out - both my parents included.
@Aardvark: Well everyone has heard of "The Internet", so Mozilla Firefox doesn't really hint at all that it has anything to do with the Internet, it sounds more like a game or something.