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I've had problems on both linux & win2000/win2003 but I've managed to get it to work on both.
The really nice thing is MySQL itself, it has no problems moving databases between OS's, different versions of mysql, the "dos" interface works the same on either system
being able to edit the mysqldump file has been a lifesaver.
The 2 big advantages that I see that linux has are.
1. It generally free
2. Its easier to turn the system into an "appliance", ie you can give a customer a complete solution, and all he uses is a web interface, no need for a monitor, keyboard.
I've been running MySQL on windows servers for 3-4 years, and they've been basically problem free.