What I found out is that you would have to use the Apple TV app to access all of your content with this promotion. It saves you money; but, the difference is in the content offerings.
For Showtime, there is very little difference between the Apple TV and the Showtime app. But, if you use the Showtime app with your subscription, you will be billed by Showtime because they are 2 different subscriptions. I was told by a Showtime rep. The Apple TV channel is not a third party biller with Showtime. The Apple TV channel also allows you to watch live tv from both the East and West coasts like the Showtime app does.
However, there is a large difference between the CBS All Access channel and the app. With the Apple TV channel you only have access to what content they offer. To watch the other channels that are offered through the CBS app, you must subscribe to them individually in the CBS All Access channel. Live tv is only available on the app if it’s available in your area. (I just cannot get the app to find my correct location because I use a mobile hotspot for internet.)
Personally I’m thinking about keeping my CBS All Access account because for the fee, you have access to CBS, BET, MTV, Comedy Central, Nickelodeon, Smithsonian channel, and access to the live feeds for Big Brother. Apple TV has yet to offer this at the price of $5.99/mo or $9.99/mo (no ads.)