Importing to the USA:
The manufacturer of the equipment would need to supply you with a country of origin statement if the equipment is made in the USA, was sold overseas and you are bringing back to the US. To ensure taxes are not imposed you will also need to provide a copy of the original export documentation. Without these 2 docs, you will most likely be charged duties & taxes.
Regardless of the duties, you will still be charged for Customs Clearance + taxes that may apply (in addition to Duties).
VAT only applies within Europe if buyer & seller reside in the same country and the equipment is shipped within the same country.
Each country has different rules about taxing exports and about export paperwork- most countries do not charge taxes on export as they try to encourage it to improve their exchange balance with foreign countries.
Finally I would recommend you to verify with the company providing service on the equipment if they will service it if your bring it in from another country.