It's only controversial because it's dressed up in wooey vagueness

I also happen to think that under-specification of this puzzle adds significantly to the controversy.

What the puzzle doesn't tell us is the properties of the universe in which it is set. Namely, whether the universe permits future to influence the past, which I'll refer to as "future peeking".

(alternatively, whether the universe somehow allows someone within the universe to precisely simulate the future faster than it actually comes - a proposition I don't believe is ever true in any universe defined mathematically).

This is important because if the future can't influence the past, then it is known with absolute certainty that taking two boxes won't possibly change what's in them (this is, after all, a basic given of the universe). Whether Omega has predicted something before is completely irrelevant now that the boxes are placed.

Alas, we aren't told what the universe is like. If that is intentionally part of the puzzle then the only way to solve it would be to enumerate all possible universes, assigning each one a probability of being ours based on all the available evidence, and essentially come up with a probability that "future peeking" is impossible in our universe. One would then apply simple arithmetic to calculate the expected winnings.

Unfortunately P("future peeking allowed") it's one of those probabilities that is completely incalculable for any practical purpose. Thus if "no future peeking" isn't a given, the best answer is "I don't know if taking two boxes is best because there's this one probability I can't actually calculate in practice".