Rob,
Moodle itself is written in the PHP scripting language with database and webserver support. There is no 64 bit "Moodle" that I'm aware of. The PHP compiler/module, the DB and underlying OS can be 64 bit, but the Moodle code itself is not 64 bit. The Moodle code itself is actually plain ASCII text, and is the same for any CPU / Bus bit count.
So to answer your questions as best I can:
1. My preference is Linux - I use RHEL / Centos. Note that as mentioned elsewhere, when you go 64 bit, everything needs to be 64 bit, but that is how it comes with RHEL / Centos ISO.
2. Course migration from one Moodle instance to another, even on the same machine involves the backp - restore function within Moodle. As long as the Moodle version is the same, and the identical third party external modules and blocks are installed, then there should be no problem, as this process is dependent on the Moodle "application" itself which is "bit agnostic".
3. Performance gains are relative, and will depend upon the new hardware, the new OS, any changes to the PHP and Webserver 64 bit version, whether you are, or have been using PHP accelerators etc. With the latter installed, you are more dependent overall on the efficiency of your hardware and database, as PHP compilation occurs less often.
For some more info, check out this thread ...
http://moodle.org/mod/forum/discuss.php?d=68845
regards
Gary