I am currently training at UKFT, California and after being here more than 2 weeks I am still unsure what I can do with this JAA "compliant" license.
Coming to the US is a wise choice in regards to number of hours you get. I am doing a completion and have done more hours in 2 weeks that I have done in over a year of my PPL in U.K.
If coming to the US to train, think wisely on where you are going and make sure your getting the right license for you.