This would be a hell of an epic battle, I'd love to see it in some sort of crossover comic some day. I'm going to have to think about it a bit before casting my vote.
I went with Phoenix because I'm more a Marvel fan and since I see it as basically a draw, I went with Marvel. I will change my vote if presented convincing arguments for why Anti-Monitor would win.
This battle could be a multiverse ending battle if it ever took place.
i'm going with Phoenix, but I'm not fully certain either. Here's why. Can the Phoenix Force act on its own or is it always within a host? If it must be within a host (presumably human like Jean Grey/Rachel Summers) then it would be limited by the hosts morality and ethics. That is the only way I could see Phoenix Force losing..