Recent changes to the Steam client seem to have introduced this problem for users of Wine on Linux. Some component of the Steam DRM or Valve Anti-Cheat system is doing a lot of a certain operation that Wine has no efficient way to implement on Linux. It doesn't affect the Mac because Wine does have an efficient alternative there.
Other users on other threads (TF2, IIRC) report that opting into the Steam beta client fixes the problem.
Dawda, I think your issue must be something else. First, running Steam native vs. via CrossOver is so different that any problem that affects both is likely external to both. For example, if your GPU overheats and the OS responds by reducing the clock speed, that would explain it. So would something having to do with your network.
If you can reproduce it under CrossOver while running a game in windowed mode, then please use Activity Monitor in the background to identify if CrossOver Games, wineloader, or wineserver is using lots of CPU. If so, you can try sampling those processes which are using significant quantities of CPU and submit the sample reports in a ticket. (Actually, it's better to use the "sample" command from the command-line with a delay, because you want to sample the game while it has focus and is running. So, identify the process ID then issue a command like "sleep 10; sample <process ID>" in Terminal. While the 10-second sleep is happening, switch back to the game window and resuming playing to the degree possible. Then the sample will occur while the game is doing its thing.)