Err, yes you can, sort of. It's the piggyback licence and effectively allows you to exercise the privileges of the FAA licence as long as you maintain your JAA licence (or CAA, as in my case).
Benefit? You can fly in the USA. If you fly an N-reg machine, you can fly in Europe (you can fly your n-reg heli in the UK on your European licence, but only in the country of issue). There may be others, but that's a start. The only cost is £39 to our lovely CAA to provide a form that discloses what qualifications you have and a trip to an FSDO in the USA (I used Los Angelese while I was passing through. No charge from the FAA.