I was recently troubleshooting some IE issues with a customer when I discovered they were using 64-bit IE clients, ..., yes I was surprised too. So for those that may not know, only 32-bit IE 6 and IE7 are supported by SharePoint, as you can see from the link below:
Plan browser support (Office SharePoint Server)
AFAIK, only 32-bit ActiveX controls were shipped with the Office clients to provide SharePoint integration, which means only 32-bit IE can take advantage of those ActiveX controls. 64-bit Windows provides both 32-bit and 64-bit IE.
One other tidbit, keep in mind that the next version of SharePoint will require 64-bit servers, check the link below for more info or just check out the exerpt below...
Windows SharePoint Services 3.0 and Office SharePoint Server 2007 are the last SharePoint Products and Technologies versions able to run on 32-bit hardware and operating systems. Do take this into account in current and future hardware decisions: Buying 64-bit hardware today helps ensure that your environment can accommodate future requirements and helps you to take advantage of the performance and scale of 64-bit technologies.
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