On a quick look, it seems the main difference is that the Hugo vote rounds always eliminate one candidate at a time, whereas the New York vote rounds can eliminate all named candidates with too few votes to have a chance of winning (which in this case would be all candidates below the top two by the time you get to round 3)?
I can see why NY does it that way (among other things, it speeds up the process), but it is interesting to see how the preferences shift in the Hugo rounds.