Pay particular attention to both Rosalyn's and Frank's points, all of which I agree with.
First, you have to figure out if there is anything in the duty free shop that actually interests you. You will see that most of what they have to sell are things like liquors, cigarettes, and perfumes - items that traditionally had high duties. I've never seen anything in a duty free shop that interested me, as their selection is quite skewed.
Next, you have to see if the duty free shop prices are actually bargains. Nowadays, these items are often the same price or cheaper when bought at home, so there's no need to schlep them back from Europe.
Next, be aware that duty free in Europe does not mean duty free in the United States. You still have to declare any items in excess of the amount that US customs allows to be carried in duty free, and you may be assessed US duty on these items.
Finally, Rosalyn is quite correct about the security procedures. If your first airport of arrival in the US is where you will be ending your trip, then you can carry on items from the duty free store in Europe and not have any trouble in the US. However, if you are changing planes in the United States, you have to go through customs and immigration at your first airport of arrival in the United States. You have then left the secure area, so you have to go through security again. Any items that do not meet the carry on rules will have to be moved into your checked luggage before you recheck your bags at your connection airport, and before you go through security again. Otherwise, that bottle of liquor will have to be discarded.