It's like Dumbledore says in PS, I think, that Snape has always disliked Harry, but he never wanted him dead. Clearly Snape is capable of great violence because he was a DE, but there are plenty of situations where he can be angry without wanting to kill anyone.

Of course, the thing with Sirius was when they were kids, which could also be a factor. He may still remember it as he was back then, when it was more about Sirius being able to do anything and still have everybody think it was sort of cute. So it's not necessarily about murder but humiliation, and the way Snape wasn't important enough to make that much of a fuss over.