I don't know why it is in my case, but I suspect it's because Wine and/or the AMD drivers on Linux don't implement as many visual effects as there are on Windows, which makes the game easier on the GPU.
If you use Wine to play DirectX 9 games, try the d3d9 fork. It's a fork with patches that give a much increased performance with DirectX 9 games which aren't merged into the Wine mainline because of the usual bikeshedding reasons. I use it to play WoW and I get better performance than on Windows.