I used to spend a lot of time with the drawknife reducing large staves down to near net shape. But lately I've been forcing myself to get more aggressive when splitting staves out so that I have as little material to remove as possible. This sometimes means I screw up and waste some wood, but it also means that sometimes I get more staves out of the same log than I would have if I'd have been more conservative. Its a give and take.
Anyway, Once I've split it down as far as I dare, I take to it with a drawknife and hatchet depending on the stave and my disposition at the time.
I've never liked the rasps I have, but I'll admit they are cheap and probably not made for heavy wood removal. If I invested in a better rasp, that might change my strategy.