A recent study from Digitalsmiths, a Tivo-owned research company, showed that twice as many movies are viewed from Amazon Video than on iTunes. This may be shocking news, because iTunes is a very popular service; however, this fact may prove the importance of having your content available on multiple devices rather than locking it to just one set-top box.
Amazon Video also has content that iTunes does not—from Amazon original programing to Amazon Prime. Though smaller than Hulu and Netflix, Amazon Prime Video streaming still offers a large number of titles including HBO content.
The other part of this may be that iTunes is only available on iOS devices that are primarily phones, tablets, and iPods. It is possible that most people want to view movies on a large screen. With Amazon Video being available on more TVs, DVD players, game systems, and streaming set-top boxes they have a larger market available to them.
Whereas many people are willing to watch shorter videos on their phone and even the occasional movie on their tablet when travelling, the majority of viewers prefer watching movies on TV. Because iTunes is only available on the Apple TV, iTunes is limited in their ability to reach people where they want to watch their content.