The classic unhelpful response: it depends.
OK, a little more helpful now. Most software doesn't benefit directly from the change to 64 bits. Very large databases can make use of the extra memory that is directly addressable, and apps that make heavy use of fp math will benefit too, including games. AMD's chips have more to offer than this though. You should see a performance advantage on just about all non-trivial software, since in 64 bit mode the Opteron and Athlon 64 chips have extra registers available, and it's this that improves the performance of most software. Debian and Gentoo are working on AMD64 ports, you might want to look into those before paying for SUSE, Fedora too I think. I don't know what state any of these other distros are in though, others may know more. Hope this helps some.
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Steve