“Apple says that app developers on its mobile devices don’t have to do anything to enable AirPlay, though they can disable it. By contrast, Google is working with each developer to enable Chromecast. Also, the mirroring feature, which only works with computers on Chromecast, also works with iPhones and iPads on AirPlay and Apple TV.
In addition, of course, Apple TV has built-in content sources that don’t require a mobile device or laptop. These include iTunes, Netflix, YouTube, Hulu+, Major League Baseball, and photos and music you’ve stored in Apple’s cloud services. Chromecast has no built-in media services.
One big advantage Chromecast has over AirPlay is that, once you start streaming something from your device to the TV, you can switch apps and do other things on the device, like check email, without interrupting the stream.
With AirPlay, in most cases, you can’t do that, although there are some exceptions, like HBO GO. Apple says this capability is up to the developer.
A big reason for this difference: On tablet and smartphone apps, Chromecast isn’t beaming directly from the device, but is using your tablet or smartphone to trigger delivery of the content from the cloud to Chromecast, freeing up the device. Apple says AirPlay also supports this method, but most app developers don’t seem to be using it, so the iPhone or iPad is usually tied up beaming the content to the TV.
This reliance on the cloud instead of the device is also why Google has to work developer-by-developer to spread the use of Chromecast, while Apple doesn’t.”