My character takes care of the people that serve him faithfully, treating them all equally(no discrimination towards aliens), and will always help out a loyal member of the Empire. He himself is very patriotic when it comes to the Empire. However if you cross him/betray him or try to get in his way he will kill you. When it comes down to it he will even kill Vette(his wife) if she tries to betray him. So when Quinn betrayed him one of his most trusted allies he just wanted to choke the life out of him(hell so did I LOL). Therefore it was very disappointing when you weren't given the choice to do that.
Since then Ive come up with a couple of reasons as to why my SW might have left Quinn alive. Just to make it clear, if I havent already, my Sith Warrior does not have a romantic relationship with Quinn so I wont include romantic reasons.
-Firstly Quinn was still useful, despite his betrayal. He was a great tactician who could operate both on the battlefield and outside it.
-Secondly he was the best healer in the Sith Warrior's crew. Now I know that some people think this is not important, story-wise, but I have to disagree. The Sith warrior(at least my one) knew how important Quinn was on the battlefield and how valuable his skills were.
-Lastly he decided to give Quinn a chance to prove himself again, to prove that this betrayal was his first and last one. And in my opinion, to some extend Quinn did prove that he is from that point on loyal to the SW and to the SW only. This is firstly seen when while you are on Correlia. If you decide to leave Quinn on you ship to defend the Dark Council member who was going to help you defeat Baras( cant remember his name), then when the assassin comes to kill the Dark Council member it is said that Quinn was the first one to attack the assassin and the last one to retreat if I remember correctly. But for me Quinn really proved his loyalties when I had him on my side when I was fighting with his old master(Baras). Quinn didnt only stand by and watched how i killed his old master he also helped me during the battle. I think that really proves that after you spared him(someone like Baras wouldnt spare him) he becomes your loyal servant.
All of this said if I had the option I would have killed him. And if there is an option in the future where you could kill him off for his past crimes then he is going to die for betraying me despite the fact that he had proven himself after the stabbing in the back.
P.S. the reasons that I gave may apply to only my SW as other Sith warriors may have different "personalities/views".