IE 32-bit is more compatible with more websites and the 32- bit version can use flash (although there is a beta version of Adobe flash 64-bit). There are other factors such as add-ons and extensions that only work for 32-bit or 64-bit respectively. Some technologies are yet to work with the 64-bit version of IE. Microsoft recommends using the 32-bit version.

You can read more about the differences between the two from Microsoft here:
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