We are going to setup a new system for our MySql server (v5.1.58) and currently we are choosing between Windows 7 x64 Ultimate and Windows Server 2008 R2 Standard.
Do you think we may get any performance increase if using Windows Server 2008 R2 (comparing to Windows 7)?
Well, Win7 is a client and 2008r2 is a server. While they share the same code base, I'm pretty sure I'd stick with the server. It's what it was designed for after all.
If you're worried about upfront cost, you have to figure that Server was designed with system tuning and client connections in mind. Win7 isn't. You'll be better suited in the long run paying the cost now instead of pulling your hair out later because you cheaped out in the front end.