My answer will be based on my experience as I made no benchmark to prove what I say.
First I think that if you have a correct machine something like a i5 and 4GB or ram performance shouldn't be an issue on both platform (If you run Windows Server 2008 this should be the case!).
Now for If performance is really important for you I would clearly advise Linux for several reasons.
Bitcoin uses a lot of open source dependencies like leveldb, Boost or QT.
This libraries are mainly primarily coded for Unix environments and also probably optimized for them.
For example I worked with leveldb and there is no official release of leveldb work Windows. You have to path it by your own to get it working on windows.
leveldb (the database that stores the unspend output) may use a lot of ram 1GB or more. The advantage of Linux is that the operating system doesn't consume a lot of RAM (About 500mb for Debian more then 1GB for Windows 7 after start).
Generally you get better performances if you compile a program from it sources instead of installing it from it's binaries.
This is possible as well on Linux as on Windows but compiling bitcoin on Linux is much easier.
I personally run a bitcoin server on a Debian 6 machine with an Intel Atom processor and 2GB of ram. It is running fine.