My personal understanding on the matter is that regardless of the licence you hold, you need to have a Medical accepted by the national Authority of the place you are going to fly in.
Supposing to fly somewhere in Africa with a JAA licence on a registered EU aircraft (for bush flying), do I only have to pass a local medical examination? What about licence conversation or other paperwork?
Regarding JAA medical Vs FAA a big difference between the two is that with the former a visual requirement is to reach 6/9 vision with glasses in each eye while the latter requires 10/10 each eye with glasses. That's my limitation.