Right from apple.com
- AirPlay Mirroring to Apple TV (2nd and 3rd generation) at 720p
- AirPlay video streaming to Apple TV (3rd generation) at up to 1080p and Apple TV (2nd generation) at up to 720p
- Video mirroring and video out support: Up to 1080p with Apple Digital AV Adapter or Apple VGA Adapter (adapters sold separately)
- Video out support at 576i and 480i with Apple Composite AV Cable (cable sold separately)
If you're using AirPlay for video with the new ATV3, you're going to get 1080p. If you're using Mirroring, it will be 720p regardless of ATV generation. Sorry.
Well, here you are another link "Right Now 1st Jan, 2013 Right From" the Apple Store
Apple Store said:Video mirroring and video out support: Up to 720p through Lightning Digital AV Adapter