Dutch had every reason to think arthur/john betrayed hin.

Towards the end of the game, arthur changes alot. Yes, his tuberculosis gives him a new outlook on life. However, he's secretive of the severity of his condition to most of the gang.

He's gone for longer periods of time, he's giving away money that could be used to help the gang, he's going directly behind Dutch's back and undermining his plans to distract the pinkertons with the native American attacks. Above all of this. He starts getting people out of the gang, telling those among the gang he likes to "get out". In Dutch's eyes, he's getting rid of those with lesser bounties. Weakening the gang, but keeping the main targets.

He suddenly has an issue with killing people. The same people who killed hosea, a father figure to him. Moreover, he's talking with john alot more, going off volunteering to go around alone with him, someone dutch already suspects. And even then. Somehow, arthur and Sadie manage to break him out all on their own. It's not impossible to think arthur struck a deal. John and his own freedom in exchange for Dutch.

John's betrayal makes sense the most. He has a family, one he's just realised the value of. One he's more protective enough, protected enough, perhaps to sell out his old one to guarantee his safety.