We have had Borzois with German Shepherds, but never owned a Saluki. They got along fine and never fought, even female to female, but I wouldn't say they were best buddies, not like 2 Shepherds. They did play together, but of course, the Borzois would run circles around the Shepherds, literally.
They are very different dogs, both very smart, but in different ways. The Borzois were much more sneaky and conniving, I guess you would say. Rules are meant to be broken and it's their job to find how to do that.
For example, our male was lying on the couch while a friend was eating a bowl of macaroni and cheese. The phone rang and the friend got up to answer, leaving the bowl of food on the coffee table.
When he got back, he felt something wasn't right, but nothing seemed to have been disturbed. He thought if he dog had gotten into his food, there would be nothing left, so he grabbed the bowl and started to eat again. Then he looked at the dog. Pippin had a noodle sitting right on the top of the end of his nose, looking completely innocent.