Abolishment of import duties is one of the things that TTIP is trying to establish. However, from what I can see, VAT will still be an issue in transatlantic trade.
I just imported $1450 worth of aircraft parts to the US (the other way around), and no tax or duty was payable (zero). Civil aircraft parts are exempt from US duty, and no sales tax is collected.
Having obtained an export certification I'm now trying claim back VAT paid initially because I collected the parts from the factory in Germany. It's really a ridiculous time and money wasting situation with VAT and duty in most European countries. Several times I've had stuff shipped from Europe to my US address, to avoid VAT, then hand carried it back across the Atlantic for use in Europe.