Back to the original poster; it all very much depends on what your 'problem' is.
Contrary to popular belief the FAA medical is not easier; it is different; their starting point is very different from that in JAA land.
I know of people who have had less problems getting a JAA medical issued by the CAA than an FAA by the feds.
Regarding colourvision the tower colour vision test as done by the FAA (don't know about CASA one) gives, when passed, the same level of ICAO compliant medical certificate as those that pass the Ishihara plates or JAR's lantern test.
That is the reason that FAA jocks can fly their 747s through JAR skies, not because of some 'courtesy'