Some theorize that Daedric Princes are above morals and It got me thinking; what about Barbas? Barbas warns the Dragonborn against deals with Clavicus. When you go to Sheogorath, and you report back to him telling him Pelagius can sleep well or something like that, he'll reply thinking you killed Barbas and congratulate you. As for Vile, it's fact that he hates Barbas and when you consider killing him, Clavicus will say something like; "Put him out of our misery". Notice the "OUR" there. So that might suggest that other Daedric Princes and/or Daedra hate Barbas? If so... why? In Vile and Barbas's unused Dialogue, Barbas will state; "Well, I guess you could say I got on his nerves, I tend to be the voice of reason, and he finds that irksome". Clavicus will complain about his "Incessant Preaching". Also in the unused Dialogue, if you reunited him with Barbas and clicked on his shrine again after the quest was over you had the option say; "I see he (Barbas) is having a good influence on you." And Vile would reply: "Yeah, rub it in, just imagine what I could get done with my full power and none of these pesky morals." That also suggests Barbas is constantly complaining about Vile and the nasty stuff he does. And by the ref from Sheogorath and Vile suggesting he gets on other Daedra's nerves, it sounds like he might complain about all the Daedric Princes?

So, what is it with Barbas? If the Daedra don't seem to be able to understand murdering etc... is bad, how come Barbas can?

Vile and Barbas are two sides of the same coin. You could consider Barbas as the 'good' side of Vile, but the Daedra are beyond mortal conception of good and evil.

Barbas is a good dog.

Clavicus Vile wants to shaft everyone. I wonder why anyone bothers dealing with him. Maybe Barbas is there to ensure that at least some of his deals are fair so that the mortals keep coming. It wouldn't be an ideal arrangement for Vile or Barbas, but it seems to work.