Oh, here we go again. A 'My training is better than your training' thread.
I could make a fancy JAA instructor look pretty stupid in US airspace if I was nasty enough to do so, and I am sure a JAA person could make a fancy FAA instructor look pretty stupid in Euroland too. At least the FAA instructor is almost guaranteed to have an IR. If you ever get to listen to Approach control at a US Class B airport you will hear JAA trained Virgin and JAA trained British Airways pilots making radio transmissions which are as sloppy (and safe) as their American colleagues.
Just be aware that a 250 hour instructor in both regimes really is a kid and has a lot to learn, and by the time he reaches 1250 hours, he still has a lot to learn too! Whirlybird has it right, a good instructor will get the book out and look it up with the student, no harm in admitting you don't know everything and no shame in asking for help either., no matter how many hours you have.