I think I may be a bit behind the times here, as it's been ages since I've needed to download anything big from MSDN, but it seems that by default the MSDN File Transfer Manager tool doesn't work correctly with IE 11 at the moment. When you try to download something it always just tries to do a normal browser file download, and never launches the file transfer manager, even though you have it installed.
Having done a bit of googling, it turns out that this is because the MSDN Subscriber Downloads website still uses bits of VBScript to launch the File Transfer Manager, and IE11 doesn't run VBScript any more.
You can get around this by forcing IE11 to pretend to be IE9 when you're trying to download. You just navigate to the page for the download you want and then use the Developer Tools to change the browser mode you're using. Hit F12 to open the tools, and switch to the "Emulation" tab:
Setting the Document Mode and User agent string to their IE9 options before you click download will make it all work again.
This workaround is documented in KB2900662 but to be honest, the description of the issue doesn't really tally with what I was experiencing, so it took me a while to find it.