Low latency (edit: I should probably elaborate given the community I'm in - when looking for wireless headsets specifically for use while gaming, it's an easy way to know that what I'm getting is going to be low latency, and likely come with a specific receiver for that)

Sometimes, gaming headsets introduce a specific sound signature (similar to EQ but hardware) so that certain frequencies are louder. For FPS it could be advantageous to hear footsteps, for example.