Really, when you slit the throats the birds die right away, all the movement afterwards is just reflexive. Many folks prefer to dispatch their birds this way because the still-beating heart helps pump more of the blood out -- instead of just allowing gravity to drain it out -- leaving a cleaner carcass. I've heard this called a kosher-kill.
I myself had difficulty with the chop method, couldn't get the head severed completely with one neat blow, and feared I was making my birds suffer more that way. But if you're having success and it makes you feel better about the job then by all means, chop away!