CNN does not even remotely attempt to copy Fox and they have been going downhill since Fox came on the scene and provide people with a perspective that was not all left of center and that did not favor only the Democrats and Democratic Party. So, in almost every time slot, Fox nets ratings that are more than MSNBC, CNN, and HLN combined and frequently challenges the networks. Fox takes on the stories and really investigates them that the other cable channels and the networks won't. So, even with the right leaning editorial bias at Fox, Fox is where people go for news that they can't get anywhere else.
And yes, Time Warner owns CNN though the owner rarely actually pulls the strings.