Flight Safety, CAE and Pan Am are all approved by the UK CAA, as well as Bombardier in Canada. Not sure whether anyone else has approval from other JAA states. The reason you will probably only see the big boys seeking JAA approval is the cost involved in getting the inspections done, tens of thousands of dollars a year. This also has an effect on the prices - a JAA rating done in the US will probably be a little cheaper than in Europe but significantly more than the corresponding FAA rating for the same type.