You can run a 32 bit version of a Mozilla application using a 64 bit kernel (Windows 7 x64 etc.) though a 64 bit version "supposedly" increases performance. The main reason to use a 64 bit version is if an application exceeds the 4GB virtual memory space limit. That shouldn't occur with Firefox or Thunderbird. You may get a slight performance improvement, but frequently its marginal.
This updated blog post benchmarks 32 and 64 bit versions of Firefox, including Waterfox (specifically compiled for 64-bit) and concludes that "We should see some performance improvements in the future, but Firefox 64-bit doesn't appear to give you a faster browsing experience at this time." This Ghacks article compares 32 and 64 bit versions of popular browsers and concludes "Most differences are marginal and not visible to the user. "
- Code that uses a lot of pointers will consume more memory. 64 bit pointers are larger than 32 bit pointers, so there's more memory to move around, causing a potential performance hit. The effective processor cache size will also be reduced.
- Code that is not careful about memory packing/alignment can run less efficiently as 64 bit.
- Code that uses large data types (64/128 bit WORDs) will be faster because you don't need to play the 'split it into 32 bit WORDs' game.
- A 64 bit version might be faster due to it being optimized for CPU's that support x86-64 (it has twice as many general purpose registers and SSE/SSE2 registers as a x86 CPU, and they're all twice the width).
The Firefox and Thunderbird download pages now support downloading both 32 bit and 64 bit builds. For Firefox click on the "Advanced install options & other platforms" link. For Thunderbird click on the Systems & Languages link.
While its recommended you download the setup program from the normal download page you can also get them from http://releases.mozilla.org/pub/ or http://download-origin.cdn.mozilla.net/pub/ (preferred). You need to do this if you want a setup program for a 64-bit build before Firefox 43 or Thunderbird 60.
Many Linux distros provide their own 64 bit builds of Firefox, Thunderbird, and SeaMonkey in their repositories.
Forcing a automated update (using Help -> About Thunderbird or Tools -> Options -> Advanced -> Update -> Check for updates) works for 64 bit release builds of Thunderbird. This was confirmed by the update from 60.0 to 60.2.1.
Tracking bugs: Windows x64
Windows 64 bit builds in Thunderbird
64 bit Windows package for Lightning
Third Party Builds
WaterFox and Pale Moon are optimized 64 bit versions of Firefox for Windows. Start64 and Firefox 64 have several 64 bit builds of Firefox (nightly, WaterFox etc.) for several operating systems. .
The Third Party/Unofficial Builds forum has optimized 3rd party builds that may include some 64 bit builds for Windows.
Extensions and themes
Most extensions and themes don't care what operating system you are using, or whether you are using a 32 bit or 64 bit application. Its mainly an issue for the Lightning and Enigmail add-ons for Thunderbird. Lighting was originally a separate add-on, then a bundled add-on, and is now part of Thunderbird.
You can not use a 32 bit build of Lightning with a 64 bit build of Thunderbird. There are official 64 bit builds of Lightning available for Linux and OS X but they're for nightly builds. Nightly builds are automated untested builds . Unofficial 64bit builds of Lightning for Linux are available at here. Also look in the contrib subdirectory of the latest release in releases.mozilla.org
You need to use a 64 bit version of a plug-in if you use a 64 bit Firefox build. The Adobe and Foxit web sites auto-detect whether you use 32 or 64 bit.