I one-box on Newcomb's. I two-envelope on this. This situation, however, is absurd. [ETA: Now that I think about it more, I'm now inclined to one-envelope and also more irritated by the hidden assumptions in this whole hypothetical.]
Omega's prediction is bizarre, because there's no apparent way that the contents of the envelope are entangled with my decision to accept the money - whether I am the kind of person who two-boxes or one-boxes, the contents of the envelope were decided by a coin toss. It seems the only way for Omega to make a reliable prediction would be to predict my response to Omega's deal, and then phrase the deal such that my predicted response is tied to the actual contents of the envelope. That is, Omega knows the envelope is empty, and he knows I will accept the offer, so he says "reject offer iff envelope is full."
In other words, I don't actually believe Omega can reliably make this same prediction, as he could theoretically do in Newcomb's; this hypothetical is absurd. If you had a thousand people, roughly half of them would have opened envelopes full of money (or whatever percentage would emerge from Alpha's random generator). It seems inconceivable that those half must also have rejected the ten pound note, and that the other half must have accepted it. If I saw a large enough sample illustrating this effect occurring consistently, I'd have to throw up my hands in confusion and reject the ten-pound note, but this outcome is outlandishly unlikely.
(replying to new version of comment) Yes, Omega could easily only offer the deal to those for whom his prediction is true.
This is a variant built on Gary Drescher's xor problem for timeless decision theory.
You get an envelope from your good friend Alpha, and are about to open it, when Omega appears in a puff of logic.
Being completely trustworthy as usual (don't you just hate that?), he explains that Alpha flipped a coin (or looked at the parity of a sufficiently high digit of pi), to decide whether to put £1000 000 in your envelope, or put nothing.
He, Omega, knows what Alpha decided, has also predicted your own actions, and you know these facts. He hands you a £10 note and says:
"(I predicted that you will refuse this £10) if and only if (there is £1000 000 in Alpha's envelope)."
What to do?
EDIT: to clarify, Alpha will send you the envelope anyway, and Omega may choose to appear or not appear as he and his logic deem fit. Nor is Omega stating a mathematical theorem: that one can deduce from the first premise the truth of the second. He is using XNOR, but using 'if and only if' seems a more understandable formulation. You get to keep the envelope whatever happens, in case that wasn't clear.