What countries like both JAA & FAA on you license?
It is not about any country requiring or "liking" both.
You increase you job opportunities because you can go "either/or"
In some regions of the world there is a preference for either/or and some countries may not care at all and a validation is easy for either one.
When we say "Complete"the IR back in Europe, do we mean just the IR test?
Theoretically you can but practically your cahnces of passing are very slim without at least some transition training into different airspace with different procedures and requirements.
If you hold a ICAO CPL ME-IR and you have passed the 14 ATPL written exams a practical conversion plus skill tests will set you back somewhere between $12,000 and $15,000.
Depending on the school you go to.