"They hit us, so we hit them back."
That's the nature of the business - the Family Business. Santino was not a psychopath - he never got his hands dirty, so far as I know. I read the novel, but don't get a notion that Santino actually committed murder by his own hand. Ordering hits is another thing. It's almost like a game.
I think Sonny did do hits personally. I believe that the book states that he came in under Clemenza and showed a preference for the gun instead of the garotte.
But in the part where the Don is temporarily out of commission during the "Irish war" I'm pretty sure that it states something along the lines of (paraphrasing)- "Sonny showed a genius for urban warfare and made a name for himself as the most cunning and relentless executioner the underworld had yet seen, though for sheer terror he was surpassed by Luca Brasi".
Carlo is said to be quite aware and be very afraid that Sonny would kill him naturally, like an animal and think nothing of it. He envies Sonny that. And Hagen thinks of Sonny kindly and thinks that the fact that he was a violent and cruel murderer was irrelevant. In book remember that Sonny volunteers to be the one to meet with Sollozzo and Hagen dismisses it b/c Sollozzo wouldn't be stupid enough to let Sonny within a mile of him.