There are pro's and con's to doing it either way but if I had to do it all over again, I'd get the JAA knocked out first and then the FAA

One thing to keep in mind; The JAA is no longer, I think and EASA is now going to be actioning any changes in Flight Crew Licensing. Years ago I thought I'd be able to do a conversion course from FAA to the UK CAA ATPL, which used to exist. Then the JAA came into being and there was no longer any short cut to getting a Euro ATPL.

Do the EU license now and everything else will be easy in comparison.