In physics general relativity and quantum field theory are applied to different domains and at least one, possibly both, are widely recognized as mere approximations to the ultimate theory that subsumes them.

I'll defer to Dr. Miller on this if he cares to weigh in, or any other professional economist, but my outsider's impression is that in economics as discussed by Romer the situation is more that contradictory theories are being applied to the same domain, without a serious effort to determine experimentally which (if either) is correct.