"AirPlay lets you wirelessly stream what’s on your iOS device to your HDTV and speakers via Apple TV. Or mirror exactly what’s on your display to the big screen. Vacation photos, blockbusters, the latest games — AirPlay and Apple TV put it all on your TV."
As for Chromecast and Miracast, At this time, you can not say which one is better or which is not good. They are two different devices that are used in different ways. Miracast cuts the cable between your devices, while Chromecast is more of a stand-alone dongle that allows streaming on its own. I think they are both great.