This is a common topic. My opinion is clearly in the minority- but, here it is...
Any type of screw will hold securely if it is used in the right material and has the right size pilot hole. There generally isn't a very large range of hole sizes that a given thread will grip securely.
Therefore, I have no problem with self-drilling screws; by design, they make the right size hole for the threads. {I would have a problem with a self-drilling screw being used in a pre-existing or deformed hole).
While drywall screws are not sheet metal screws, I have a problem with them anchoring anything, unless they are "pulling" into the wood they were designed to pull into (or light steel framing, as the case may be!)
As for the size of the screw as it relates to the ability of the screw to carry current, I suspect that head size is more important than screw diameter or material thickness- what we need to do is connect as much wire area to as much metal area as we can. (We also need to cut through the paint).
