If I had to guess, I'd say Alpharius is very intently trying to carry out the original plan of "Make Horus win, destroy Chaos, ????, Profit!" while Omegon is having second thoughts and trying to see if there is another way to win the war.
Of course, this could just be the mindset of the Alpha Legion so ingrained into them that they just don't know they're "striking from multiple ways" in that Alpharius is trying to win one way and Omegon is trying to win another way but neither of them really trusts the other enough to speak about it. Chaos is screwing with these guys too, it seems.
I wonder if at some point Alpharius tries so hard to destroy Chaos that he accidentally ends up "joining" them, or at least doing what they want, whereas Omegon is trying to help the Imperium and so remains "loyal."
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