The margin between the cost in Europe and the USA is not as large as you might think, the USA aircraft cost may be low but look hard at the small print regarding taking the aircraft away from base and don't forget to factor in your living expenses.
This is very misleading. If you actually do some research to find an FBO with decent rates and low daily minima, the difference in prices is enormous. When I lived in Europe I'd often come and do 2-3 week flying trips in the USA, taking camping gear and often sleeping under the wing. Accommodation every now and then is very cheap, if you get fed up of camping.
As an example, in the Netherlands my club charged 270+ Euros for a Piper Arrow (and this was back when Euro was about 1.4 dollars). In the US, I pay $124. If you want to fly more than a few hours, the costs of getting here get wiped right out.
The flying environment is also much nicer. Better ATC, more accessible airspace, more predictable weather, and the airports (with no fees) are far better equipped than anything GA tends to see in Europe. Many airports actually have a vibrant GA community who'll welcome you and show you around; Europe, not so much.
Having flown about 50-50 between Europe and the USA, USA wins hands down for the actual flying, and lack of hassle. Europe wins out for pretty and interesting cities to visit.