AMD64 (both AMD and Intel CPUs support it; it's not the only 64-bit architecture which I use) is faster, but uses more memory. It is needed to access more than 1 or 2 GiB of virtual memory in a single program, or to efficiently use more than 1 or 3 GiB of RAM for all programs. I use 64-bit systems on all my computers with compatible processors, and 2 GiB of RAM is enough for them. (Other architectures have ways to have some speed benefits available in 64-bit mode without using more memory, but it isn't commonly supported for AMD64.)
There were compatibility problems years ago, but most programs currently support AMD64, many not needing any changes except recompiling, and it works in Trisquel without noticeable problems. Not sure how it is done in Trisquel, but it is possible for existing 32-bit programs to run without changes (using more space for separate 32-bit libraries needed for them and not combining 32-bit and 64-bit code in one program). Some distros recommend not using 64-bit systems, since they use non-free software supporting only 32-bit x86. We don't have this problem here.
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