As someone who has both JAA and FAA licences,
I am more than happy to say that JAA is of a higher standard of flying, although the FAA is a higher standard of knowledge. (For USA schools unless you trained at Oxford where the CPL standard is dubious)
The JAA IR is the equivalent to the FAA ATP - regardless of approaches. The local DPEs where I trained were both JAA and FAA qualified and whole heartedly agreed with this consensus.