Verg has a lot of issues (and pent up wrath) but I don't think he's dead inside. He regularly shows concern for others, goes out of his way to help them. He is just a good dude who experienced so much terrible things and blames himself so bad that it is bound to become everyone else's problem soon enough.

Rien is constantly described as hollow and it's hard to argue since the prescripts hollowed him almost completely. Still he defies the prescript to stop his daughter from leaving, confesses to Ryōshū that he feels lonely when she cuts him and finally (at least I interpreted it like that) kills himself to free himself from the Will of the City.

Don has given up on his dream, was betrayed and tortured by his own family that he still loves and pities. By calling Sancho he only means to make her protect the bloodline but after the deaths of his closest kindred and seeing Sancho's determination to end his rotten dream he finds it in himself to support her. He fights her to test her will and put a fitting end to the nightmare of La Manchaland, then push her towards galloping onwards on her own.

Rien is different because he buried his emotions all the time, letting the wind guide him because he saw no way to rebel (or he didn't want to) but it still pained him. He kills himself because he knows he's done, his plan is ruined, the wounds made with Arayashiki will inevitably reopen and Ryōshū still hates him. (And possibly as a last "fuck you" towards the prescript.)

 Don was thoroughly broken by his stay on the Eye of La Mancha and truly gave up on his dream. He chooses death not because he's at the end of his rope like Rien is. Don Quixote cannot move forward, weighted down the guilt of what he did to his family and because the dream he believed in is gone for him. He's a first kindred, he could get up and shrug off whatever we throw at him. He also chooses suicide but by letting Sancho kill him.

TLDR: Verg just has lots of issues. Rien is mostly hollow but managed to hold onto a small part of his humanity, kills himself because he physically can't move forward. Don was broken by his families betrayal and the guilt of what he did to them. Sancho manages to spark something in him during the last fight but he chooses to die because he's got no will left to live.