Sling TV, HBO Now, and other apps unstable except on mobile devices sums it up.

UPDATE: 2016

SlingTV and HBO Now are fairly stable on Android and iOS devices but on the Amazon FireTV Stick, it seems to be a blackhole of freezes and resets somedays. I've come to the conclusion that Amazon FireTV is good for one thing and that's Amazon Prime and Amazon provided content. Third-party apps seem unstable consistently.

However on Chromecast, when casting from my iPad or Android phone it works flawlessly. One caveat however, I believe that your mobile device needs to support HD 1080 video for it to cast HD video to Chromecast.