Opportunity in the US should be good for years to come. But don't waste any time if you're going to come here, seniority is moving fast and the sooner you get some the better off you'll be.
I would probably decide where you're going to work first. If it's the US do your training here, for US certificates. That will help with English and be cheaper and likely faster than doing EASA training. If you change your mind later, you can always convert (either direction), but I probably wouldn't do the conversion unless you get to a point where you need to.
Based on your written English, you should be fine here, especially if you train here. US employers (including airlines) cannot (and do not) discriminate based on English skills. Any accent doesn't matter, as long as you can understand and be understood. You just get an English language endorsement on your certificate once and then you're good forever. If you have a green card, FAA certificates, and competitive experience you'll have the same opportunities as anyone else. Worth noting, that does NOT work both ways, I would have a very hard time getting a job with a good airline in Europe.