FAA will be cheaper, you could do it in half your budget in the USA. Do NOT pay all your money upfront. The written exams are easier in the USA also. If you want to get a degree after your flight training, I know people who got their commercial license and instructor rating and went to University and taught flying lessons on the weekends and after class at the local flying school.
For what it is worth, if you ever think one day you will work as a pilot in Europe, get your JAA rating, it would save you the conversion later. Also, in the USA, the airlines don't really give preference to nationals, it Oshkosh hard for foreigners to get rights to live and work, it is like winning the lottery to get a greencard (literally, the greencard lottery).
In Canada, there is a reality documentary show called Ice Pilots, and there is even an Indian guy who just got hired at the flying company, so anything is possible.
There are lots of wonderful places to do your training in the USA, but there are also some really shady places. Like I said, don't pay your money up front. If some place wants you to pay up front, go somewhere else. Also, don't get caught up in the word Academy in the US. A small school or large Academy, it doesn't make much of a difference, most important is the maintenance of the aircraft, quality of training, and how you are treated as a customer. Send me a PM if you have any questions.