The way I see, think back if you've sliced yourself with a sharp knife while cutting veggies or doing dishes (my two favorite times to cut myself on accident). The pain doesn't start for a good bit, and it hurts a LOT more the next day than it does when it happens. I like to think that for a chicken, that pain won't set in for a few minutes or more- and by that time rolls around, the chicken has passed away.
I personally don't trust myself with a hatchet, and some days don't trust I would have the strength to make a clean, complete cut with one. I'm more comfortable with knives than I am with hatchets (in any circumstance, let alone processing), so I go with the process that I'm confident in. Either way, when done correctly there should be minimal suffering and pain for the chicken, but it more depends on the processor. I would bet I would botch a hatchet job and cause undue suffering, whereas someone who is confident with a hatchet might botch a jugular cut and cause suffering. Neither of us is better or worse, we're just more comfortable with one skill over the other.