I am Danish but live in Sweden, and just recently bought a house in Aruba. I too go shopping in the US several times a year, so I can compare from a Scandinavian viewpoint

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Aruba is really Paradise on Earth, but not when it comes to shopping.
Don't expect anything like a US shopping experience.
There are some nice shops, including LV, Gucci and other designer brands, including US brands like Ralph Lauren, Hilfinger etc.
But don't expect the US bargains. I would say that most prices are in between US and Scandinavian prices, so still good, but not great.
Electronics stores are few, with poor selection and relative expensive.
Jewelery are very good priced, if you avoid the ones in the malls and go on the streets instead and pay around a third of the listed price.
Booze is cheap, food are around Swedish prices if you go to the better quality stores like Ling & Sons.
So to sum it up, ANYWHERE is cheaper than Norway where a small pizza is $30

, but come here for the beaches, the weather, the people, (better than anywhere else) and make a stopover in Miami for the shopping, then you have the perfect plan.
Have fun in Aruba, but be warned.....The 20 hour journey and the $2.500 plane ticket will not be enough to keep you from wanting to come back year after year after year.
Carsten