Suggest you have a look (search) at the FAA 'based-on' license threads in the Private Flying forum on here. There's loads of info. Doesn't seem too complicated, though (don't know from personal experience, I have full standalone FAA and JAR tickets).
As a general rule, flying in the US is A LOT cheaper than in Europe (FYI in Spain they've just gone completely mad with landing fees and mandatory handling charges). I would definitely go to the US rather than Europe.
Btw, why not Oz? I know, flying ain't cheap Down Under, but if you factor in all costs, travel, etc, ??