Since nobody is answering I will share my experience with Parallels. I have never tried Crossover, so no insight from me there.
Parallels runs super with many operating systems, Linux, Windows, Chrome. You can even run a different copy/version of Mac OS X if you want.
Parallels is able to use bootcamp, so if you install Windows in a bootcamp partition first, and install Parallels afterwards, it can use that partition to run Windiws inside Mac OS X. This makes it possible to choose how you want to run Windows, as a native OS or piggybacking inside Mac OS X.
I use Windows under Parallels almost daily for clients who use Windows software that I need to access. So far I have never run into programs that have problems. Including Steam and GoW.
So if you installed everything the way it should, then it might be that there is a more specific problem. For example, GoW is an Adobe Air application, so make sure you have installed the latest version from www.adobe.com.
Hope this helps. Don’t hesitate to ask me if you need any more help.
On a side note: I am still wondering why there is no Mac version of GoW, since Adobe Air is also available for Mac OS X. But apparently it’s not that easy. Perhaps the devs can say something about that, and maybe they have a Mac version coming up, @Sirrian, @Nimhain or @Full?