As a Caius fanboy I'm gonna have to stop you there and say that what he represents is more than just Dysley or even Ragnarok!Fang.
I'm also a big Caius fan, so I don't mean to imply he is only Dysley and Fang, but thematically he takes a lot of the same points.
Caius is like Fang because of the relationship with Yuel/Vanille, and the lengths they would go to prevent suffering. And the sad part is, they aren't even ensuring a happy life, just them not being fucked over for the rest of eternity. Their entire lives are spent to ensure that they could do something for Yuel/Vanille, and it never mattered what Yuel/Vanille wants. Caius outrights says it and Fang even
raises her hand to Vanille in the last minutes of the game, not out of hatred or frustration but because there was nothing left for them to do.
What ends up being different is not that Caius is fundamentally more "evil" and Fang more benevolent, it's just that Caius turns out to be broken and Fang never crossed the line of no return. Caius and Fang are both good people, willing to get their hands dirty because the one person they loved more than anything would suffer, and they went against the world because hey- Yuel/Vanille
was their world.
Caius persona isn't like Bart but as far as they do their business, they both wait for hundreds of years, playing multiple hands. Caius and Bart differ in one way that Caius has multiple plans running simultaneously (get Noel to kill him, kill Etros in Valhalla, or get Cocoon to fall)- it's even more interesting once you note that the only reason that Noel was able to destroy the heart was BECAUSE he started on his journey, while Bart has one plan where he manipulates all the players (he is the government, he is the power that checks the government, and he is rebellion against the government, he leads Lightning and co, and he knows how to play the people).
The other issue is that Caius and Bart, despite pretending to be the wise, almost logical person with all the knowledge, they are both more emotionally affected than they let on. Bart tries to explain that this is the only way to save people, and he is doing it for all life, and that this is the way things should be. But when he dies before he gets to his third form, he's actually shouting in both happiness and relief about how he finally has sweet release, which says to me that he's really wanted this above all else.
Caius is more emotional throughout the story, he is openly hostile to Noel and sheds tears over Yuel, but he spends a decent amount of time calmly and coldly explaining to Noel why and what he is doing- like he's trying to make you see the truth. He does the same thing to Serah in the Void Beyond. During the fight on the airships, he starts out to talk about Yuel's fate, and the more he talks the more visible agitated he gets himself. Then in Valhalla, the dude finally just rages at Noel, and it's my absolute favorite part because it's a compelling villain!breakdown and it shows that calm resolve is just hiding hundreds of years of frustration, bitterness, and desperation.
Also, like Dysley, despite being the puppet master, he's also a bit of a experiment by a cosmic power above him. While Dysley wants to be with it and Caius wants to destroy it- they still are working with the issues handed down on them. Neither Dysley or Caius want power, wealth, or to rule anything. And all things considered Dysley and Caius are both immortal and can transform into huge asskicking robots/dragons that shoot fuckoff lasers, but yet as players we understand they get the crap end of the deal. Because in the end, they aren't in control of the situation they were put in, they had to struggle with their places too.
Actually that point could extend to Fang too, as the only character that fully embraces her focus, she doesn't do it for herself. And I think the game might have implied that she didn't even have to worry too much about it considering her brand is all messed up, but she still pushes to get it complete. For Vanille.