@filtronetics: The difference is more significant as the increasement of desired frequency.
@myem: Using 'air' or 'vacum' for airbox in HFSS doesn't matter.
PEC material is used for 3D objects, Perfect E boundaries is prefered to use for 2D objects.
It's the best way to simulate your ground structure with 3D object and assign its material as Copper or some others that are used in fact. (even PEC material if you want)
In the case of simulating your 2D ground structure, ofcourse, assign it as Perfect E boundaries.
Cheers!