Short Answer - You wouldn't notice on modern hardware.
The major benefit here will not be speed but relative performance for the cost.
Open source projects are usually designed and tested on *nix (linux/unix/bsd) first, and then 'ported' to Windows. Features usually creep into windows 2nd, not first.
This brings me to my next point...
Licensing fees are the hidden performance cost
If you have a 6 core Linux server it doesn't cost any money to use all 6 cores, and with the money you save on licensing you can buy more memory, or faster disks - this will be the biggest performance increase, not one OS vs Another.
Linux has unique features
There is also the case to make about Operating System features, although many programs don't yet take advantage of them...
In the case of epoll vs select() or poll() - windows does not have an equivelant, nor does it have sendfile, or a threads implementation similar to pthreads in 2.6+ Kernels.
Memory and Disk are always the Bottleneck
Processors are SO fast nowadays, processors are eternally starved (yes starved) for data - the system memory is usually 3 - 4 times slower still to this day. The processor usually does 4-5 wait cycles for every memory access. This is why processors have 3 levels of internal caching (L1, L2, L3) to help with this. Disk access will be even a larger factor - so save your licensing pennies and buy more memory, and faster disks!!!