Having done it the other way, I can offer the following:
PIC time logged in your FAA log book, that was actually with an instructor. Is not allowed as PIC in the JAA. I actually had a PIC shortfall, for the hours I have, as ALL dual is counted as dual and not PIC. PIC will be allowed when you are solo, or when PIC in a multi crew situation.
For the good news though, I have found that XC is more easily built under JAA , asin the US you need, I believe, 25 nm straight line distance AND a landing