Debugging forward is better when you have a small dataset,
I’d say the difference is about something different (trust/belief/etc.). Maybe it’s hard to find people who, upon seeing a proof whose conclusion they disagree with, actually examine it for the flaw. (Or people who want proofs.) Experimentation may enable finding ways to improve, working through everything logically may enable finding the optimal/closed form solution, Fermi estimates enable finding the order of magnitude of an effect (though this isn’t distinct from experimentation).
I’d say the difference is about something different (trust/belief/etc.). Maybe it’s hard to find people who, upon seeing a proof whose conclusion they disagree with, actually examine it for the flaw. (Or people who want proofs.) Experimentation may enable finding ways to improve, working through everything logically may enable finding the optimal/closed form solution, Fermi estimates enable finding the order of magnitude of an effect (though this isn’t distinct from experimentation).