Solcal there isn't much difference as far as I can tell between the flavours.
If you have a low hours FAA license you won't/can't get it converted and same with a JAR license.
You have a couple of thousand hours multi crew time and its a paperwork exercise for both types and an airlaw exam. The only thing that JAR licensed folk seem to have an advantage on is that all ratings are command ratings so there is no additional training required to swap to the LHS if you have only flown it RHS before. Company training and LPC and off you go.