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One difference between 32-bit and 64-bit versions of Firefox for Windows is that the latter will restrict plugin access through the use of a whitelist.

Mozilla plans to put Flash on the whitelist, and maybe also Silverlight according to the official bug report on Bugzilla. Additional plugins are not mentioned which means -- subject to change as always -- that Java for instance won't work in 64-bit versions of Firefox for Windows because of that restriction.