I don't think the difference will rely on Wordpress, but more on the server's PHP processor. Depending on the scale and volume of traffic your site will incur, your PHP processor will be the more reliant for success.
There's a few tests of running PHP on Windows vs Linux I have posted below. Google search for 'php performance windows linux'
The data concludes that in regards to the way PHP performs on these platforms, Linux would be the choice for better installation.
p a e s s l e r . c o m / w ebstress/sample_performance_tests/comparing_php_script_performance_on_linux_and_windows
b o i n c . b erkeley.edu/dev/forum_thread.php?id=566
p a e s s l e r.com/webstress/sample_performance_tests/comparing_php_script_performance_on_linux_and_windows