Distances can't be the same. If one rigs it so that distances between things look about right, the countries will be the wrong shape and that couldbe measured. If it was of course, the FE people would say it was fake... like everything else known in the world.
This could be measured... that is to say, if one draws two concentric circles on the FE map, one 1000km from the edge and one 1000km from the middle, in the RE they would be the same distances, and in the FE they'd be totally different distances.