It looks like maybe the flicking method is faster--it sure looks more fun!
I have regular cards, the kind you use two at the same time. I often find myself doing the "almost-carding" when I'm mixing a few colors of roving together in small batches. It just feels faster to use one, rather than two, because I don't have to keep reaching for the other card.
I never would have thought to brush with it! Does it wear away at your clothes to brush the roving?