3 things will get you a job, you only need one.
- Being in the right place at the right time. You have to make this happen, and you do it by applying to jobs and hopefully one of your CVs lands on the right desk.
- knowing someone on the inside
- being a naturally gifted pilot, you will never struggle for a job.
Having trained myself in Europe, I only know a handful of FAA to EASA converters, they're all jobless right now but so are the majority of Euro trained pilots I know of. I would think its better to train in Europe to become a pilot in Europe, but that's just a guess rather an experience talking.
Swings and roundabouts.