Broadly speaking, to use Apple TV as a replacement for cable, you have to be willing to give up certain channels, live sports and news, and much first-run stuff. However, if like me you found yourself watching very little of this sort of thing (or are willing to wait a day for certain shows), then Apple TV + podcasts works out very well indeed in my view.
I cut the cord on cable quite some time ago, and really the main things I miss are Turner Classic Movies and Canada's Knowledge Network. A subscription to Global BBC iPlayer ($80 a year) gives me great stuff I never even had for the most part when I had cable, and podcasts or iTunes purchases make up the rest.
I would estimate I save about $600 a year compared to having cable. But again, I'm not a sports fan and read more news than I watch, so I'm well-suited for this lifestyle.