Think ahead.......you said that you'd like to "turn it into" a CPL eventually. Do you have the right to work in the USA? There isn't much work for an FAA CPL in Europe (private/corporate jet stuff is about all).
You are probably best to do the JAA course and find somewhere that can give you a "double checkride". Have both, why not?
Whatever bit of paper you get there will be a checkout to do before anybody rents you their aircraft. So from that point of view there isn't much difference.