Based on experience with 3rd-generation AppleTV (Apple TV Software 6.2 (based on iOS 7.1.2) Wikipedia), I have concerns about the privacy of my usage behavior. Not from Apple per se, but from the 3rd-party apps.
AppleTV has the same "Reset Advertising Identifier" setting as iOS devices. Other than the setting to "automatically send information to Apple from Apple TV", this appears to be the only privacy setting on the device that would affect personal data leaving the device.
Other than IP address (which I can change and/or proxy), and Advertising Identifier (which I can change), are there any other data points that a 3rd-party app owner (or its own 3rd-party ad/tracking code) could use to persistently identify me or my device, and/or track my usage over time, and/or correlate my AppleTV usage behaviors to usage behaviors on other devices?
Some additional background: Some 3rd-party apps require activation from a separate computer/browser. The AppleTV app displays a unique code to be entered on a URL associated with the app owner. This appears to be a mechanism for the app owner web site to (in some cases verify a cable/satellite subscription, and) address the specific device for activation. It's not clear if there are additional privacy implications for this process.
Also note that iOS devices also have a VendorID that is consistent for all 3rd-party apps on a particular device made by the same vendor. This can be reset by (temporarily) deleting all apps from that vendor from the device. There is no similar mechanism for AppleTV.