Another thing to consider is your lack of citizenship.
Although you are a Green Card holder, and therefore completely entitled to work here, many companies will not call you for an interview until you become a US citizen. It's completely illegal and very discriminatory, but unfortunately it is widespread and very hard to prove. The post 9/11 flightcrew scrutiny here is rediculous, and as a non-citizen you will be subject to TSA incompetence at every training event you attend. This causes you to be a hassle for the airline, compared to a US citizen, and many large employers here are simply not hiring green card holders to remove this little problem from their ranks.
It seems most regional airlines here follow the law and hire green card holders, but I know for a fact that the majors that are hiring are not taking any non-citizens. I believe Fedex and UPS require citizenship, but my understanding is that is legal for them as they have certain government contracts that state Citizens must perform the work.
Stay in BA mate, you will be better off in my opinion. The "land of the free" is not what it once was.............