They both support AirPlay these days, I've never been able to use Google Cast natively with a TV here, which is a shame for my use cases (Netflix doesn't support it, and I generally don't like to have my phone connected to the TV via Wi-Fi for the entire duration of a movie).
Edit: Turns out LG is currently in the process of adding it, and Samsung seems to have support in some models as well, but it's definitely not ubiquitous.
What's frustrating in this thread is how many people are conflating the weird dongle product with the extremely successful streaming control protocol. Only the weird thing is being cancelled!
Chromecast first gen was in 2013.
Apple actually beat Google on this one in terms of time.
Come on man
Practically, this means that you can take phone calls, hibernate your computer, kill a source app on your phone, leave the house entirely etc. with Chromecast without interrupting whatever's playing on a TV or stereo, while with Airplay, playback usually stops in these scenarios. Airplay is also a bigger battery drain as a result, in my experience.