I actually wonder why people here keep comparing prices for goods from their home country to those same items bought here. Of course a Maine lobster will be cheaper in Maine, and although they are by far the best, the local lobsters ain't bad and you pay a fraction of the cost for them.
Of course NY is more expensive than SD. Every important major city in the world is. You cannot compare NY (Wall Street), Brussels (NATO and EU-headquarters), The Hague (International Court), London ( amongst others the Beers diamond cartel), and others to SD.
The real question is how much a comparable life-quality would cost in SD, in comparison with another capital in the world. And there are 2 possible answers to that question.
The first answer is more expensive if the family involved, insists on copying their lives back there 100%. Meaning wearing the same clothing labels, eating exactly the same food (all imported then), going to the same gym's, driving the same high quality cars and buy them new, living in the same quality of house, etc... There is nothing wrong with that, but then it will indeed be more expensive to live in SD.
The second answer is cheaper if the family involved, insists on living the same quality of life they had back there, but are open-minded enough to adapt themselves and enjoy the local advantages. The quality of the local foodsupplies is fantastic, nevertheless a lot of expats insist on buying only imported pork, or pineapple in a can, etc... Where in any of the cities mentioned above can you go out and have a lobster dinner for 15$ a person. I know in Brussels it would cost me more to eat a lousy lasagna. Where in NYC can you get a coctail for 2$?
If you move to another country, in my opinion, you will have to sacrifice certain home comforts, but in return you will get others. It is up to you whether you want to do that or not. If not, you are living in the wrong country.
Myself, I love it here. Most things I do miss are a number of food-items which are impossible to get here. The famous North Sea shrimp, the fresh Dutch mussels, etc... So, whenever I go back to Belgium, I gorge myself on those. And I stuff my luggage with all kinds of goodies. Would I trade my life here, to go back to Belgium? No way.
Anyways, all the expats living here because they were placed here by their respective companies, should not complain too much I think. Whenever my company sent me somewhere I got an expense account which was more than enough to live in luxury.