Going to a school such as AIC, Macleans, Kings, Ags SKC etc it seems like several people get selected to go to ivies (and more) each year from these schools alone. So if one went to these schools, are they competing with each other?
In contrast, if one went to a lower decile school, maybe one like edgewater, would it be an advantage coming from that school since you’ll be the only one or one of the only people applying?
Likewise, it’s easier getting dux/head girl/better ranking at a lower decile school than a competitive school such as Ags, do they take into account situtations like these?
Hey - great question!
It’s clear - as you pointed our, that it is easier to get the top positions at slightly less competitive schools and obviously succeeding in this way at high school will make your application stand out when it comes to applying to colleges.
BUT on the flip side, I know that private schools like Kings/ACG etc offer an extremely large range of other opportunities which would allow you to build your application further also, even if you didn’t wind up getting one of the major positions (dux/head boy/girl).
To sum up, there probably isn’t a ‘best’ situation high-school wise, when it comes to your college applications. I would say that if you’ve done well academically, and expanded your range of extra-curricular activities, and also worked in a leadership position or on a leadership project - then you are on the way to success in your application, regardless of what school you go to. 
Bear in mind that US colleges usually also aren’t super clued-up about NZ high schools, so it’s unlikely that they’ll take it much into consideration!