What is the practical difference, though? From the point of view of the entity whose atoms have been replaced, I don't think that the speed of replacement has any noticeable effect. And the previous versions are all "extinct" regardless of the speed, so from the point of view of any previous versions, the situation doesn't change either.
Not to be obtuse, but... the speed.
Really this is a shortcoming of the thought experiment. Progressive replacement is subjectively more continuous than complete replacement. A better thought experiment would be to feed it out something like:
* What if we replaced every atom of you body progressively over 24 hours?
* What if we replaced every atom of your body suddenly all at once?
* What if we replaced every atom of your body, but delayed by 1s?
* What if we replaced every atom of your body, but delayed by 1 day?
* What if we replaced every atom of your body suddenly all at once, but moved about 1mm?
* *What if we replaced every atom of your body suddenly all at once, but a day later and moved by thousands of miles?"