I would absolutely go FAA. The problem is, I don't think the pilot market would have improved by 2021 in EU or the USA. I know of some people who did their flight training in the USA and then stayed on for 12 months after and worked as CFIs. It's usually only for colleges grads but I know of 2 people who did it after flight training. I think the programe is called OPT.
Another problem is alot of instructors and too few students at US flying schools atm.