Having completed the conversion last year from FAA FI to JAA Fi I would definitely recommend it.
If you are going to live in the UK/Europe it is defintely something to fall back on. At first I was irritated at the number of ground hours having already accrued large number in the FAA world, however, I really found the JAA approach different and useful.
When it comes down to it, where are you going to be living? Plus, passing the JAA FI, will make the FAA FI a breeze which you would be able to add on in minimal cost to complete the CV!