Amazon limits the resolution to 720p and audio to 2-channel stereo on all iOS devices such as iPhone, iPad, etc. However, the Amazon resolution is not limited when using an Android device (android phone/tablet and any media player that uses Android O/S such as the Zappiti or Zidoo players). If you know for a fact that the resolution is not limited on AppleTV, then maybe it is the exception. NOTE: that the AppleTV could still be outputting 1080p or 4K to the TV, even though the Amazon app is limiting the resolution internally.
As regards to Erik's statement. I have evaluated the Amazon FireTV cube. It is surprisingly good for a small device that uses a switching wal-wart power supply. However, the sound is a bit bright and harsh. I compared this to a TIVO unit that is using a Teradak linear power supply and tested Amazon streaming. The TIVO unit with linear power supply just blew away the FireTV cube in both video and audio quality. Video was sharper and more saturated and bolder in color. Audio was extremely good without any harshness. Both of these were tested using the same HDMI cable into the same TV.
Also, not all HDMI cables are created equally. They all have different results in both video and audio.
As regards to Erik's statement. I have evaluated the Amazon FireTV cube. It is surprisingly good for a small device that uses a switching wal-wart power supply. However, the sound is a bit bright and harsh. I compared this to a TIVO unit that is using a Teradak linear power supply and tested Amazon streaming. The TIVO unit with linear power supply just blew away the FireTV cube in both video and audio quality. Video was sharper and more saturated and bolder in color. Audio was extremely good without any harshness. Both of these were tested using the same HDMI cable into the same TV.
Also, not all HDMI cables are created equally. They all have different results in both video and audio.