I will check my settings tonight, BUT I believe it depends on your TV. I'm at the office and as such I can not connect my iPad to my Apple TV. Generally as I recall it depends on what you are watching and on how it is broadcasting. Netflix for example should take up the whole screen, BUT if you are doing a mirror of your screen to see your browser on the big screen THAT might be in letterbox.
It depends on what you're watching and/or how you're watching it. For example, if you're "mirroring" a game that only plays in portrait mode, it will not fill the TV screen. Many games that play in landscape mode will fill the entire TV screen. In regard to videos, turning the device to landscape mode can help, but a majority of the videos I've watched via AirPlay on my ATV fills the entire TV screen whether in portrait mode on the phone or not.