I'm curious what people are aware of for experiments or tests that will differ depending on belief of RE or FE. FE needs to be falsifiable after all. Here's the ones I can come up with in my time, along with what I've seen discussed in regards to them so far. I would love it if FE believers would be up for giving any more, or correcting my 'conclusions' on the ones posted here.
1) 'Sinking ship'
a) FE posits that a ship whose hull has 'vanished' from sight, can be restored by the use of optical magnification. Videos have been posted purporting to show this effect, largely argued to be inconclusive evidence from RE proponents.
b) RE posits that a ships hull vanishes from sight by going over the curve and cannot be restored using magnification. Videos have been posted purporting to show this effect, largely argued to be inconclusive for similar reasons.
Conclusion: None. Neither sides evidence has been conclusive enough for the other.
2) Lasers/spotting over distance
a) FE posits that a laser shone from a level position across a surface (such as a lake) will arrive at the other side at the same height that it left. Youtube is littered with these videos, but RE mostly regards them with skepticism both for the general lack of experimental rigor, and the unknowns of firing a laser over water.
b) RE posits a certain amount of drop should occur depending on the distance the laser is fired. One video in particular has been offered up, the laser part of the experiment undergoing intense scrutiny. Unfortunately exactly matching up with mathematical drop calculations has left it in a problematic state for being able to reject the FE videos as well.
Conclusion: None. Neither sides evidence is particularly conclusive, and b leads to problems in dismissing a.
3) Horizon to eye level
a) FE posits that the horizon will always rise to eye level. There have been few images/videos shown in reference to this, the largest proof for it residing within EnaG. RE proponents generally regard the statement with skepticism and request photo's showing the effect with detailed information about how it was done.
b) RE posits the horizon should 'dip' lower and lower beneath 'level' as one goes higher. Currently a thread is underway working to create current images to prove this. FE proponents have been largely silent here recently, but expressed concerns over the setup of the experiment near the start. One FE experiment suggestion was met with skepticism by RE crowd.
Conclusion: Unknown at present. Information is still being gathered and is yet to be fully presented. As well, FE proponents have yet to set forth a structured set of what they would accept as proof.
4) Add your own
There should likely be more, but these are what I can come up with for relatively easy/cheaply testable differences. Do note, there are a number of things that, while the mechanisms are different, the final observations are stated to be the same regardless of flat or round. Including but not limited to: Sunset/rise, appearance/disappearance of pole star(s), separate constellations, movement of the stars, and angle of the sun.
I invite FE or RE to correct if I've presented something wrong, or if they have more differences to offer. The best differences would be those that can be tested relatively cheaply or easily by one person, ideally both.