What's interesting about these two movies is that both men are essentially fighting for themselves. Wyatt Earp takes up arms against the Cowboys after his brothers get involved in preventing crime to protect them, and the Cowboys kill one of his brothers and maim the other. In High Noon, Kane is fighting for his life. 

But these are examples of likable, heroic lawmen fighting for admittedly selfish, but justified reasons. Both Red Dead Redemption and Red Dead Redemption 2 play up the cause of the outlaw—In Red Dead Redemption, John Marston is trying to be a good man, but his past catches up with him, and he is extorted by corrupt FBI agents to hunt down his old gang. In Red Dead Redemption 2, Arthur Morgan is an outlaw and a murderer (the extent of which largely depends upon the player), but he mostly tries to do what is right (though, again, this depends upon the player). But the Pinkerton agents that chase him and his gang are metonyms for the corrupting influence of progress for progress' sake, and they are merciless. In different ways, both Martson and Morgan are metonyms for the pleasures and power of freedom without the constraints and bureaucracy of civilization, and because the player must live within and interact with the world as the characters, the player is exposed to a more visceral, immersive experience of the freedom and violence of the outlaw. Granted, this can be problematic, but for the creators of the Grand Theft Auto series, the moral conflict present in the Red Dead Redemption games is a giant leap forward for morally complex storytelling. 

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Both of the Red Dead Redemption games are influenced by The Wild Bunch (1969), but whereas The Wild Bunch is about a gang of vicious outlaws set up against equally vicious people with power and authority, Red Dead Redemption and Red Dead Redemption 2 force their protagonists (and many of the tertiary characters) to be conflicted about their actions and violence, even if it is sometimes justified. 

 

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One interesting example of a story about an outlaw and a lawman with (nearly) equal claims to justice is Hell or High Water (2016). In this Western set in the contemporary world, both Toby Howard (Chris Pine) and Marcus Hamilton (Jeff Bridges) have reasons to want to kill the other. Howard wants to start a new life for his family after escaping poverty because of his crime spree with his brother, and Hamilton wants revenge for the death of his partner (caused by Howard's brother). But both are fundamentally decent men who are unwilling to settle the confrontation in front of Howard's family, and the scene (and movie) ends in a stalemate that is postponed until a later time.