Which wall mounted ones do you have? Is there any srill involved? Size capacity it holds and cost?I can't speak for this particular model but I have the wall mount version and it's awesome. Full articulation, stable and easy to install. I'd try and find the manual for it and see if it states the min and max thickness of the desk it requires.
I seem to think you get two versions, one that clamps on and another that you drill holes through your desk for. Best to check their website to see if they have any manuals for that particular model