The mirroring performance of the Fire TV is on comparable to the Apple TV (low latency, high quality). Chromecast (which uses WebRTC) has noticeable quality issues, on both audio and video.
I never actually got around to sending the audio output to the Apple TV, so the Fire TV implementation is the best of the 3 currently.
Summary of the three platforms:
Fire TV – Great audio and video quality. Works on any 4.4+ device.
Apple TV – Great video quality. Great audio quality, but I don’t have audio implemented yet.
Chromecast – Good video quality after 2 minutes, when WebRTC ramps the bitrate up. Terrible audio quality, not sure why. I think that it encodes the audio stream to be optimized for voice. Requires a hardware vp8 encoder, currently only available on Nexus 5.
Boldfaced emphasis added by me.
Well, I didn’t know that about Chromecast with AllCast. Time to think about Fire TV.