You point out perhaps the only potentially meaningful difference, and it is the main salient point in dispute between one-boxers and two-boxers in the Omega problem.
First subpoint:
With Omega, you are told (by Omega) that there is certainty—that he is never wrong—and you have a large but finite number of previous experiments that do not refute him. Any uncertainty is merely hoped for/dreaded. (There are versions in which there is definite uncertainty, but those are clearly not similar to the OP.)
Second subpoint:
If there is truly, really, actually no uncertainty, then correlation is perfect. It is hard to determine cause and effect in such conditions with no chance to design experiments to separate them. I’d argue that cause is a low-value concept in such a situation.
You point out perhaps the only potentially meaningful difference, and it is the main salient point in dispute between one-boxers and two-boxers in the Omega problem.
First subpoint: With Omega, you are told (by Omega) that there is certainty—that he is never wrong—and you have a large but finite number of previous experiments that do not refute him. Any uncertainty is merely hoped for/dreaded. (There are versions in which there is definite uncertainty, but those are clearly not similar to the OP.)
Second subpoint: If there is truly, really, actually no uncertainty, then correlation is perfect. It is hard to determine cause and effect in such conditions with no chance to design experiments to separate them. I’d argue that cause is a low-value concept in such a situation.