IE 32 bit has the broadest compatability because of many available add ins while IE 64 offers some better security in part because of fewer available add ins.
Some add ins (like Plugins and Toolbars) are only available in 32 bit versions and will not work in 64 bit IE. Some are available in both x86and x64 and automatically install in both IE x86 and IE x64 by running one installer. Other addins have separate installers for x86 and x64 and need to be run separatly.
If you click on the Start Menu and the choose All Programs you should see in the list "Internet Explorer (64 bit)" and "Internet Explorer" which is the 32 bit version
Hope this helps
Ed