I think most of the GPU-based bitcoin farmers are using desktop hardware, but I might be wrong.
One is the tiny ancient GPUs used to drive VGA outputs on servers. Those are hardly even worth talking about; they're only there so that you can hook a monitor up in an emergency.
And then there are real server GPUs, like nVidia Tesla stuff. Those typically don't even have video outputs, but they're on par with modern high-end gaming GPUs, possibly even better at some tasks.
I believe most bitcoin farmers are still using desktop GPUs, but that's largely just because they're running relatively simple kernels, all things considered, and because desktop GPUs are cheaper and easier to source.
Also, AMD tends to be more cores at a lower clock rate than nVidia. For embarrassingly parallel integer operations (like hashing) AMD blows nVidia out of the water.