OK so I've thought of an experiment that could prove this one way or the other. According to the FE mumbo jumbo we can't see real far because of the atmosphere. Well that means that there is a maximum distance we would be able to see.
So here's what we need: a ship/boat/something that will float, binoculars or something and a big tower with ocean views.
And here's what we do. We stand on the shore (so as to be at sea level) and send the ship out to the horizon. From there we go up our big tower and, using the ship as a reference point, see how far we can see. According to the FE theory we shouldn't see as far (since the line of sight to the ship would now be longer), and by RE we should see further (think of it as seeing further around the earth because of your elevation).
And that's it. Now, fly my pretties! Fly!