This is a three way battle, and Starz! Made a strategic mistake when they cut the streaming deal with Netflix.
Studios were unwilling to cut deals directly with Netflix because they threatened their already existing relationships with the cable and premium networks. Netflix did an end run around this with their deal with stars!. However the content gained from that deal showed the potential in streaming, and the studios have grown more willing to talk to Netflix, which the networks fear. Also, Netflix is beginning to act more and more like a proto-network, eating up syndicated shows, b movies, and just starting to look at a small number of flagship original programing.
With their dividing of the into two distinct and separate divisions, they no longer have to treat both parts of the company the same. It's smart. They can build the streaming side as the first true internet based tv replacement model, without the anchor of the DVD-by-mail rental business holding that change back.
Also, keep in mind that epix just signed a deal with Netflix, so that may have carried some weight in stars! decision to pull out.