The advantage of the quick drain plug is convenience not speed (irony in the name, eh?). Plus you don't need to safety wire the quick drain after each oil change so you pick up some time there. I place a plastic tube around the quick drain nipple when I'm ready to drain the oil and place the other end into a plastic oil drain pan I purchased at an auto supply store. This way I have only a few drops of spilled oil by the time I'm finished. I use Van's quick drain. It works fine and costs half of what the one in the Spruce catalog costs.
Regarding the oil screen, this can be a real mess because of its location, usually there is something like a cable bracket in the way that will keep you from doing a clean job. Depending on whom you talk to, the oil screen doesn't have to be drained each time. In fact some people do it only once to check that there are no tailings in there from the manufacturing process. Of course if you don't have a spin on oil filter, then you drain from the oil screen every time.
If you have a taildragger, you might consider getting a "Tail-Mate" or some other method of leveling the airplane. Using this, I can change the oil and filter on my RV-8 without having to climb up on a ladder. The level position seems to make changing the filter easier and cleaner, too.
Chris