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Fight takes place in a neutral city (neither has knowledge of)

Both have access to the same weapons cache.
A shotgun, an AR-15, two 9mm handguns, and a knife.

Anton wins if he is in personification of death mode and makes Vincent flip a coin for his fate.

Barring plot devices, Vincent wipes the floor with Anton. Chigurh is probably my favorite villain in film history, but the majority of NCFOM saw Anton kill unsuspecting civilians and surprise a group of Mexican cartel members in a motel room. The one time someone was expecting him (Llewelyn in the hotel), he was tagged by a shotbtgun and had to escape on foot.

Vincent has similar unsuspecting assassin murders under his belt, but also has the alleyway 2-on-1 handicap match where he murdered two men, one of which had a gun on him, and the nightclub scene where he fired his pistol while moving in on the Asian gangster, fired from a downed position, and utilized a knife and CQC when one of the gangster's bodyguards got a hold of him.

Vincent takes this one, Collateral is a fantastic movie, but No Country is better IMO.

Great analysis! I'm inclined to agree with you. It seems Vincent is more of a tactical operator that has no problem dealing with trained guards etc.

Anton does well against thug cannon fodder but I'm not sure he'd fare well against a highly trained enemy.

One point where Anton really shines is his willingness to go thru whatever pain to get the job done. Whereas Vincent I can see dropping the job if he doesn't see the value in it. I'd love to see the fight tho.

I'd pay money now to see it on the silver screen, but yes they are very different movies. Both are two great antagonists, though Vincent is more of a protagonist villain (Michael Mann's style, see Heat and Public Enemies), whereas Mr. Chigurh is a straight psychopath antagonist.