My experiences shooting box birds have left me thinking, concerning choke, that you're damned if you do and damned if you don't. A more open choke on the first shot may kill the bird dead or it may cripple it. If it cripples it maybe you have made it a bit easier to hit it again with the next barrel, and tighter choke. However, if you miss with the second you may be SOL, because it can often climb the fence and be a lost bird.
Many top shooters who shoot two tight chokes live by the mantra "Waste the first shot", meaning to take the first shot so quickly that you may indeed miss clean.
I enjoy the game immensely but just cannot shoot enough to be competitive.