First off, Internet Explorer 8 and Internet Explorer 9 are both available in 32 & 64-bit so you are mixing things up a bit.
The fact is that even though IE 8, 64-bit came out with W7, many add-ins like flash, etc were not available till roughly a year ago. Therefore W7 was set up to automatically default to the 32-bit version whenever you click email or shortcut URLs; the only way to get the 64-bit version to run was to open it manually.
Even today, some add-ins are only available for 32-bit browsers. For example, your A/V may still not offer a 64-bit malware protection add-in for your 64-bit browsers (NORTON SYMANTEC, F-secure, and others). When you talk to their product support they tell you their product will still stop the virus once it is downloaded but if that's so fool proof then why do they have an add-in for 32-bit browsers that actually scan webpages? I digress, but basically, depending on your A/V, web pages may be less secure when visited using a 64-bit browser.
But more to your exact issue, it all depends what PDF support is loaded in the browser. Check your Tools ... Mange Add-ons ... and check the toolbars & extensions to see whate is loaded from Adobe (personally I see an Adobe PDF Link Helper & Adobe PDF Reader)