I have the same background as you. Unfortunately aviation hasn't gone the way as the maritime world where STCW has a big bearing on almost every aspect of shipping and has been adopted internationally to a large degree although you'll still get companies who insist on people who trained in certain countries.
Generally speaking, you should do flight training where you are able to work. Having said that, even though there are pockets of elitism within EASA, (won't name the countries here, we all know who they are) - commercial flight training is pretty much a pan-European thing now.
Training in North America and is still an option but it's been made such a headache to "convert" to EASA credentials that's it's just not worth it anymore, you'll probably lose out financially and spend more time doing it.
Whatever you decide to do, good luck.