AirPlay mirrors your device, which means you can no longer use it during playback and will drain its battery fairly quickly. You're also subject to network lag.

AirPlay mirrors your device, which means you can no longer use it during playback and will drain its battery fairly quickly. You're also subject to network lag. Chromecast simply sends commands to the TV/speaker, which does the streaming directly from source. You can use your device for something else.