Read through Bookworm's link. In principle you can bring your aircraft with you duty and VAT free. There are some time limits on disposing of it in the EU (which I can't remember). The ferry flight is probably about $10-15k each way (fuel is very expensive along with insurance and you will probably find you can not get insurance without having a pilot along who has done the crossing before). You probably want professional advice on the import side as HMRC has an amazingly poor sense of humour if you don't do it right! I can recommend
Here as a highly knowledgeable and effective General Aviation customs expert.
Flying over here is great from the perspective of lots of different countries to go to. However, the process is amazingly bureaucratic and expensive compared to the US. You will definitely want some help getting used to the airspace, the rules, and how IFR operates in Europe.